Showing papers on "Singularity published in 2020"
TL;DR: A general covariant modified theory of gravity in D=4 spacetime dimensions which propagates only the massless graviton and bypasses Lovelock's theorem is presented and several appealing new predictions of this theory are reported.
Abstract: In this Letter we present a general covariant modified theory of gravity in D=4 spacetime dimensions which propagates only the massless graviton and bypasses Lovelock's theorem. The theory we present is formulated in D>4 dimensions and its action consists of the Einstein-Hilbert term with a cosmological constant, and the Gauss-Bonnet term multiplied by a factor 1/(D-4). The four-dimensional theory is defined as the limit D→4. In this singular limit the Gauss-Bonnet invariant gives rise to nontrivial contributions to gravitational dynamics, while preserving the number of graviton degrees of freedom and being free from Ostrogradsky instability. We report several appealing new predictions of this theory, including the corrections to the dispersion relation of cosmological tensor and scalar modes, singularity resolution for spherically symmetric solutions, and others.
462 citations
TL;DR: In this article, the authors analyzed singularity regularization in spherically symmetric situations and showed that the set of regular geometries that arises is remarkably limited. And they also showed that there is a clear tradeoff between internal and external consistency.
Abstract: The 1965 Penrose singularity theorem demonstrates the utterly inevitable and unavoidable formation of spacetime singularities under physically reasonable assumptions, and it remains one of the main results in our understanding of black holes. It is standard lore that quantum gravitational effects will always tame these singularities in black hole interiors. However, the Penrose's theorem provides no clue as to the possible (non-singular) geometries that may be realized in theories beyond general relativity as the result of singularity regularization. In this paper we analyze this problem in spherically symmetric situations, being completely general otherwise, in particular regarding the dynamics of the gravitational and matter fields. Our main result is that, contrary to what one might expect, the set of regular geometries that arises is remarkably limited. We rederive geometries that have been analyzed before, but also uncover some new possibilities. Moreover, the complete catalogue of possibilities that we obtain allows us to draw the novel conclusion that there is a clear tradeoff between internal and external consistency: One has to choose between models that display internal inconsistencies, or models that include significant deviations with respect to general relativity, which should therefore be amenable to observational tests via multi-messenger astrophysics.
92 citations
TL;DR: In this article, it was shown that the singularity of a random matrix is 1/2+o_n(1))^n, where n is the number of entries in the matrix.
Abstract: For each $n$, let $M_n$ be an $n\times n$ random matrix with independent $\pm 1$ entries. We show that ${\mathbb P}\{\mbox{$M_n$ is singular}\}=(1/2+o_n(1))^n$, which settles an old problem. Some generalizations are considered.
82 citations
TL;DR: In this article, the flat space limit of 3-point correlators in momentum space for general conformal field theories in even spacetime dimensions was analyzed, and it was shown that they exhibit a double copy structure similar to that found in odd dimensions.
Abstract: We analyze the flat space limit of 3-point correlators in momentum space for general conformal field theories in even spacetime dimensions, and show they exhibit a double copy structure similar to that found in odd dimensions. In even dimensions, the situation is more complicated because correlators contain branch cuts and divergences which need to be renormalized. We describe the analytic continuation of momenta required to extract the flat space limit, and show that the flat space limit is encoded in the leading singularity of a 1-loop triangle integral which serves as a master integral for 3-point correlators in even dimensions. We then give a detailed analysis of the renormalized correlators in four dimensions where the flat space limit of stress tensor correlators is controlled by the coefficients in the trace anomaly.
74 citations
TL;DR: In this paper, an anti-parity-time (anti-PT) symmetric cavity magnonics system with precise eigenspace controllability was studied, and two different singularities in the same system were observed.
Abstract: By engineering an anti-parity-time (anti-PT) symmetric cavity magnonics system with precise eigenspace controllability, we observe two different singularities in the same system. One type of singularity, the exceptional point (EP), is produced by tuning the magnon damping. Between two EPs, the maximal coherent superposition of photon and magnon states is robustly sustained by the preserved anti-PT symmetry. The other type of singularity, arising from the dissipative coupling of two antiresonances, is an unconventional bound state in the continuum (BIC). At the settings of BICs, the coupled system exhibits infinite discontinuities in the group delay. We find that both singularities coexist at the equator of the Bloch sphere, which reveals a unique hybrid state that simultaneously exhibits the maximal coherent superposition and slow light capability.
74 citations
TL;DR: In this article, a static and spherically symmetric black hole charged by a Born-Infeld electric field in the novel four-dimensional Einstein-Gauss-Bonnet gravity was studied, which is intended to bypass the Lovelock's theorem and to yield a non-trivial contribution to the fourdimensional gravitational dynamics.
Abstract: A novel four-dimensional Einstein-Gauss-Bonnet gravity was formulated by Glavan and Lin (Phys. Rev. Lett. 124:081301, 2020), which is intended to bypass the Lovelock’s theorem and to yield a non-trivial contribution to the four-dimensional gravitational dynamics. However, the validity and consistency of this theory has been called into question recently. We study a static and spherically symmetric black hole charged by a Born–Infeld electric field in the novel four-dimensional Einstein–Gauss–Bonnet gravity. It is found that the black hole solution still suffers the singularity problem, since particles incident from infinity can reach the singularity. It is also demonstrated that the Born-Infeld charged black hole may be superior to the Maxwell charged black hole to be a charged extension of the Schwarzschild-AdS-like black hole in this new gravitational theory. Some basic thermodynamics of the black hole solution is also analyzed. Besides, we regain the black hole solution in the regularized four-dimensional Einstein–Gauss–Bonnet gravity proposed by Lu and Pang (arXiv:2003.11552).
73 citations
TL;DR: A cutting condition independent TCM approach for milling with vibration singularity analysis is introduced which utilized a Support Vector Machine model and a transition point identification method (TPIM).
68 citations
TL;DR: In this paper, the authors proposed to use leading singularities to obtain the classical pieces of amplitudes of two massive particles whose only interaction is gravitational, and obtained a compact formula for the fully relativistic classical one-loop contribution to the scattering of two particles with different masses.
Abstract: In this work we propose to use leading singularities to obtain the classical pieces of amplitudes of two massive particles whose only interaction is gravitational. Leading singularities are generalizations of unitarity cuts. At one-loop we find that leading singularities obtained by multiple discontinuities in the t-channel contain all the classical information. As the main example, we show how to obtain a compact formula for the fully relativistic classical one-loop contribution to the scattering of two particles with different masses. The non-relativistic limit of the leading singularity agrees with known results in the post-Newtonian expansion. We also compute a variety of higher loop leading singularities including some all-loop families and study some of their properties.
68 citations
TL;DR: In this paper, it was shown that a necessary condition for a function to be the kernel of a fractional derivative is an integrable singularity at 0, and that a function can be used as the kernel if and only if it is singular at 0.
Abstract: The problem whether a given pair of functions can be used as the kernels of a generalized fractional derivative and the associated generalized fractional integral is reduced to the problem of existence of a solution to the Sonine equation. It is shown for some selected classes of functions that a necessary condition for a function to be the kernel of a fractional derivative is an integrable singularity at 0. It is shown that locally integrable completely monotone functions satisfy the Sonine equation if and only if they are singular at 0.
67 citations
TL;DR: In this paper, the improved dynamics for the treatment of spherically symmetric space-times in loop quantum gravity was studied in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space times.
Abstract: We study the "improved dynamics" for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou {\em et al.} in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and derive the corresponding effective semiclassical metrics. We then discuss some of their properties. Concretely, the space-time approaches sufficiently fast the Schwarzschild geometry at low curvatures. Besides, regions where the singularity is in the classical theory get replaced by a regular but discrete effective geometry with finite and Planck order curvature, regardless of the mass of the black hole. This circumvents trans-Planckian curvatures that appeared for astrophysical black holes in the quantization scheme without the improvement. It makes the resolution of the singularity more in line with the one observed in models that use the isometry of the interior of a Schwarzschild black hole with the Kantowski--Sachs loop quantum cosmologies. One can observe the emergence of effective violations of the null energy condition in the interior of the black hole as part of the mechanism of the elimination of the singularity.
65 citations
TL;DR: In this paper, the authors argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020) generally involves ill-defined terms in the four dimensional field equations.
Abstract: We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside some remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions, and find that the central curvature singularity can be reached within a finite proper time.
TL;DR: In this paper, a geometric classification of all spherically symmetric spacetimes that could result from singularity regularization is presented, using a kinematic construction that is both exhaustive and oblivious to the dynamics of the fields involved.
Abstract: We present a geometric classification of all spherically symmetric spacetimes that could result from singularity regularization, using a kinematic construction that is both exhaustive and oblivious to the dynamics of the fields involved. Due to the minimal geometric assumptions underlying it, this classification encompasses virtually all modified gravity theories, and any theory of quantum gravity in which an effective description in terms of an effective metric is available. The first noteworthy conclusion of our analysis is that the number of independent classes of geometries that can be constructed is remarkably limited, with no more than a handful of qualitatively different possibilities. But our most remarkable result is that this catalogue of possibilities clearly demonstrates that the degree of internal consistency and the strength of deviations with respect to general relativity are strongly, and positively, correlated. Hence, either quantum fluctuations of spacetime come to the rescue and solve these internal consistency issues, or singularity regularization will percolate to macroscopic (near-horizon) scales, radically changing our understanding of black holes and opening new opportunities to test quantum gravity.
TL;DR: In this article, the authors provide a rigorous analysis of exponential convergence of an adaptive spectral collocation method for a general nonlinear system of rational-order fractional initial value problems.
TL;DR: In this article, a singularity of stresses and displacements in the vicinity of a mode III crack is discussed and it is shown that inhomogeneity in surface elastic properties may significantly affect the solution and to change the order of singularity.
TL;DR: In this article, a generalization of the Oppenheimer-Snyder model is proposed to describe a bouncing compact object, where the corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play.
Abstract: This article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models: if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or at most at the energy threshold of horizon formation, so that only an instantaneous trapping horizon may be formed while a trapped region never forms. This conclusion relies solely on i) the assumption of continuity of the induced metric across the time-like surface of the star and ii) the assumption of a classical Schwarzschild geometry describing the (vacuum) exterior of the star. In particular, it is completely independent of the choice of corrections inside the star which leads to singularity-resolution. The present model provides thus a general framework to discuss bouncing compact objects, for which the interior geometry is modeled either by a classical or a quantum bounce. In the latter case, our no-go result regarding the formation of trapped region suggests that additional structure, such as the formation of an inner horizon, is needed to build consistent models of matter collapse describing black-to-white hole bounces. Indeed, such additional structure is needed to keep quantum gravity effects confined to the high curvature regime, in the deep interior region, providing thus a new challenge for current constructions of quantum black-to-white hole bounce models.
TL;DR: In this article, the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space is considered, and an appropriate version of Tikhonov regularisation supplemented with the Morozov discrepancy principle is proposed.
TL;DR: In this paper, the authors proposed two new effective Hamiltonians for the reduced classical model of loop quantum gravity in the context of Kantowski-Sachs spacetime and compared them with the Hamiltonian derived in general relativity and the common effective Hamiltonian proposed in earlier literature.
Abstract: In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole and develop a classical effective description for its interior which eventually resolves the singularity. However, little progress has been made toward understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the spacetime continuation beyond the singularity, based on results in full loop quantum gravity. In this paper, we present an attempt in this direction in the context of Kantowski-Sachs spacetime, through the proposal of two new effective Hamiltonians for the reduced classical model. The first is derived using Thiemann classical identities for the regularized expressions, while the second is obtained as a first approximation of the expectation value of a Hamiltonian operator in loop quantum gravity in a semiclassical state peaked on the Kantowski-Sachs initial data. We then proceed with a detailed analysis of the dynamics they generate and compare them with the Hamiltonian derived in general relativity and the common effective Hamiltonian proposed in earlier literature.
TL;DR: In this article, the authors consider the case of a sphere made of homogeneous dust and show that the process of collapse is qualitatively similar to that of pure Einstein's gravity, where the singularity forms as the endstate of collapse and it is trapped behind the horizon at all times.
TL;DR: In this article, the authors demonstrate a simple holographic consequence of the Schwarzschild singularity, focusing on a perturbation that is uniform in boundary space and time, and show that the deformed nearsingularity, trans-horizon Kasner exponents determine specific non-analytic corrections to the thermal correlation functions of heavy operators in the dual CFT, in the analytically continued "near-singularity" regime.
Abstract: The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT by a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific non-analytic corrections to the thermal correlation functions of heavy operators in the dual CFT, in the analytically continued ‘near-singularity’ regime.
TL;DR: In this paper, it was shown that given an initial vorticity which is bounded and $m$-fold rotationally symmetric for $m \ge 3, there is a unique global solution to the 2D Euler equation on the whole plane.
Abstract: We show that given an initial vorticity which is bounded and $m$-fold rotationally symmetric for $m \ge 3$, there is a unique global solution to the 2D Euler equation on the whole plane. That is, in the well-known $L^1 \cap L^\infty$ theory of Yudovich, the $L^1$ assumption can be dropped upon having an appropriate symmetry condition. This contains a class of radially homogeneous solutions to the 2D Euler equation, which gives rise to a new 1D fluid model. We discuss several interesting properties of this 1D system. Using this framework, we construct time quasi-periodic solutions to the 2D Euler equation exhibiting pendulum-like behavior. We also exhibit solutions with compact support for which angular derivatives grow linearly in time or exponential in time (the latter being in the presence of a boundary). A similar study can be done for the surface quasi-geostrophic (SQG) equation. Using the same symmetry condition, we prove local existence and uniqueness of solutions which are merely Lipschitz continuous near the origin - though, without the symmetry, Lipschitz initial data is expected to lose its Lipschitz continuity immediately. Once more, a special class of radially homogeneous solutions is considered and we extract a 1D model which bears great resemblance to the so-called De Gregorio model. We then show that finite-time singularity formation for the 1D model implies finite-time singularity formation in the class of Lipschitz solutions to the SQG equation which are compact support. While the study of special infinite energy solutions to fluid models is classical, this appears to be the first case where they can be embedded into a natural existence/uniqueness class for the equation. Moreover, these special solutions approximate finite-energy solutions for long time and have a direct bearing on the global regularity problem for finite-energy solutions.
TL;DR: In this paper, the authors proposed finite difference/spectral methods to solve the coupled nonlinear time-space fractional Schrodinger equations with non-smooth solutions in the time direction.
TL;DR: Anti-parity-time symmetric phase transitions and exceptional point singularities are demonstrated in a single strand of single-mode telecommunication fibre, using a setup consisting of off-the-shelf components.
Abstract: The exotic physics emerging in non-Hermitian systems with balanced distributions of gain and loss has drawn a great deal of attention in recent years. These systems exhibit phase transitions and exceptional point singularities in their spectra, at which eigen-values and eigen-modes coalesce and the overall dimensionality is reduced. Among several peculiar phenomena observed at exceptional points, an especially intriguing property, with relevant practical potential, consists in the inherently enhanced sensitivity to small-scale perturbations. So far, however, these principles have been implemented at the expenses of precise fabrication and tuning requirements, involving tailored nano-structured devices with controlled distributions of optical gain and loss. In this work, anti-parity-time symmetric phase transitions and exceptional point singularities are demonstrated in a single strand of standard single-mode telecommunication fibre, using a setup consisting of entirely of off-the-shelf components. Two propagating signals are amplified and coupled through stimulated Brillouin scattering, which makes the process non-Hermitian and enables exquisite control over gain and loss. Singular response to small variations around the exceptional point and topological features arising around this singularity are experimentally demonstrated with large precision, enabling robustly enhanced spectral response to small-scale changes in the Brillouin frequency shift. Our findings open exciting opportunities for the exploration of non-Hermitian phenomena over a table-top setup, with straightforward extensions to higher-order Hamiltonians and applications in quantum optics, nanophotonics and sensing.
TL;DR: In this article, the dressed gluon and ghost propagators of Landau gauge Yang-Mills theory were calculated in the complex momentum plane from their Dyson-Schwinger equations.
Abstract: We calculate the dressed gluon and ghost propagators of Landau gauge Yang-Mills theory in the complex momentum plane from their Dyson-Schwinger equations. To this end, we develop techniques for a direct calculation such that no mathematically ill-posed inverse problem needs to be solved. We provide a detailed account of the employed ray technique and discuss a range of tools to monitor the stability of the numerical calculation. Within a truncation employing model ansaetze for the three-point vertices and neglecting effects due to four-point functions, we find a singularity in the gluon propagator in the second quadrant of the complex $p^2$-plane. Although the location of this singularity turns out to be strongly dependent on the model for the three-gluon vertex, it occurs always at complex momenta for the range of models considered.
TL;DR: In this paper, the magnetic quivers for a single M5 brane on a D-type singularity were derived for the finite and infinite gauge coupling Higgs branch from a brane configuration and the validity of the proposed derivation rules was underpinned by deriving the associated Hasse diagram.
Abstract: M5 branes on a D-type ALE singularity display various phenomena that introduce additional massless degrees of freedom. The M5 branes are known to fractionate on a D-type singularity. Whenever two fractional M5 branes coincide, tensionless strings arise. Therefore, these systems do not admit a low-energy Lagrangian description. Focusing on the 6-dimensional $$ \mathcal{N} $$
= (1, 0) world-volume theories on the M5 branes, the vacuum moduli space has two branches were either the scalar fields in the tensor multiplet or the scalars in the hypermultiplets acquire a non-trivial vacuum expectation value. As suggested in previous work, the Higgs branch may change drastically whenever a BPS-string becomes tensionless. Recently, magnetic quivers have been introduced with the aim to capture all Higgs branches over any point of the tensor branch. In this paper, the formalism is extended to Type IIA brane configurations involving O6 planes. Since the 6d $$ \mathcal{N} $$
= (1, 0) theories are composed of orthosymplectic gauge groups, the derivation rules for the magnetic quiver in the presence of O6 planes have to be conjectured. This is achieved by analysing the 6d theories for a single M5 brane on a D-type singularity and deriving the magnetic quivers for the finite and infinite gauge coupling Higgs branch from a brane configuration. The validity of the proposed derivation rules is underpinned by deriving the associated Hasse diagram. For multiple M5 branes, the approach of this paper provides magnetic quivers for all Higgs branches over any point of the tensor branch. In particular, an interesting infinite gauge coupling transition is found that is related to the SO(8) non-Higgsable cluster.
TL;DR: For each integer n ⩾ 2, the authors describes the space of stability conditions on the derived category of the n-dimensional Ginzburg algebra associated to the A 2 quiver.
TL;DR: In this article, it was shown that the singularity of the time correlation function is an equivalent sign of chaos to the maximal growth of Lanczos coefficients in the continued fraction expansion of the Green's function, and that it is due to delocalization in Krylov space.
Abstract: We analyze local operator growth in nonintegrable quantum many-body systems. A recently introduced universal operator growth hypothesis proposes that the maximal growth of Lanczos coefficients in the continued fraction expansion of the Green's function reflects chaos of the underlying system. We first show that the continued fraction expansion, and the recursion method in general, should be understood in the context of a completely integrable classical dynamics in Krylov space. In particular, the time-correlation function of a physical observable analytically continued to imaginary time is a tau-function of integrable Toda hierarchy. We use this relation to generalize the universal operator growth hypothesis to include arbitrarily ordered correlation functions. We then proceed to analyze the singularity of the time-correlation function, which is an equivalent sign of chaos to the maximal growth of Lanczos coefficients, and we show that it is due to delocalization in Krylov space. We illustrate the general relation between chaos and delocalization using an explicit example of the Sachdev-Ye-Kietaev model.
TL;DR: In this article, the improved dynamics for the treatment of spherically symmetric space-times in loop quantum gravity was studied in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space times.
Abstract: We study the "improved dynamics" for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou {\em et al.} in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and derive the corresponding effective semiclassical metrics. We then discuss some of their properties. Concretely, the space-time approaches sufficiently fast the Schwarzschild geometry at low curvatures. Besides, regions where the singularity is in the classical theory get replaced by a regular but discrete effective geometry with finite and Planck order curvature, regardless of the mass of the black hole. This circumvents trans-Planckian curvatures that appeared for astrophysical black holes in the quantization scheme without the improvement. It makes the resolution of the singularity more in line with the one observed in models that use the isometry of the interior of a Schwarzschild black hole with the Kantowski--Sachs loop quantum cosmologies. One can observe the emergence of effective violations of the null energy condition in the interior of the black hole as part of the mechanism of the elimination of the singularity.
TL;DR: In this paper, a nonlinear integrable fifth-order equation with temporal and spatial dispersion is investigated, which can be used to describe shallow water waves moving in both directions.
Abstract: A new nonlinear integrable fifth-order equation with temporal and spatial dispersion is investigated, which can be used to describe shallow water waves moving in both directions. By performing the singularity manifold analysis, we demonstrate that this generalized model is integrable in the sense of Painleve for one set of parametric choices. The simplified Hirota method is employed to construct the one-, two-, three-soliton solutions with non-typical phase shifts. Subsequently, an extended projective Riccati expansion method is presented and abundant travelling wave solutions are constructed uniformly. Furthermore, several new interaction solutions between periodic waves and kinky waves are also derived via a direct method. The rich interactions including overtaking collision, head-on collision and periodic-soliton collision are analyzed by some graphs.
TL;DR: The two phase transition temperatures are determined accurately through the singularity of the classical analog of the entanglement entropy, and extensive numerical evidences are provided to show that both transitions are of the Berezinskii-Kosterlitz-Thouless (BKT) type for q≥5.
Abstract: We perform the state-of-the-art tensor network simulations directly in the thermodynamic limit to clarify the critical properties of the q-state clock model on the square lattice. We determine accurately the two phase transition temperatures through the singularity of the classical analog of the entanglement entropy, and provide extensive numerical evidences to show that both transitions are of the Berezinskii-Kosterlitz-Thouless (BKT) type for q≥5 and that the low-energy physics of this model is well described by the Z_{q}-deformed sine-Gordon theory. We also determine the characteristic conformal parameters, especially the compactification radius, that govern the critical properties of the intermediate BKT phase.
TL;DR: In this article, an iterative method was presented to generate an infinite class of nonlocal field theories whose propagators are ghost-free, and the pole structure of such generalized propagators can contain complex conjugate poles which do not spoil at least tree level unitarity as the optical theorem is still satisfied.
Abstract: In this paper, we present an iterative method to generate an infinite class of new nonlocal field theories whose propagators are ghost-free. We first examine the scalar field case and show that the pole structure of such generalized propagators possesses the standard two derivative pole and in addition can contain complex conjugate poles which, however, do not spoil at least tree level unitarity as the optical theorem is still satisfied. Subsequently, we define analogous propagators for the fermionic sector which is also devoid of unhealthy degrees of freedom. As a third case, we apply the same construction to gravity and define a new set of theories whose graviton propagators around the Minkowski background are ghost-free. Such a wider class also includes nonlocal theories previously studied and Einstein's general relativity as a peculiar limit. Moreover, we compute the linearized gravitational potential generated by a static pointlike source for several gravitational theories belonging to this new class and show that the nonlocal nature of gravity regularizes the singularity at the origin.