Showing papers on "Singularity published in 2015"

6d Conformal matter

Abstract: A single M5-brane probing G, an ADE-type singularity, leads to a system which has G × G global symmetry and can be viewed as “bifundamental” (G, G) matter. For the A N series, this leads to the usual notion of bifundamental matter. For the other cases it corresponds to a strongly interacting (1, 0) superconformal system in six dimensions. Similarly, an ADE singularity intersecting the Hořava-Witten wall leads to a superconformal matter system with E 8 × G global symmetry. Using the F-theory realization of these theories, we elucidate the Coulomb/tensor branch of (G, G′) conformal matter. This leads to the notion of fractionalization of an M5-brane on an ADE singularity as well as fractionalization of the intersection point of the ADE singularity with the Hořava-Witten wall. Partial Higgsing of these theories leads to new 6d SCFTs in the infrared, which we also characterize. This generalizes the class of (1, 0) theories which can be perturbatively realized by suspended branes in IIA string theory. By reducing on a circle, we arrive at novel duals for 5d affine quiver theories. Introducing many M5-branes leads to large N gravity duals.

Lectures on differential equations for Feynman integrals

Abstract: Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that is based on properties of the space–time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the DE. Finally, as an application of these ideas we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a DE.

Looking for a bulk point

Abstract: We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.

The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse

Abstract: Derivation of the NLS.- Linear propagation.- Early self-focusing research.- NLS models.- Existence of NLS solutions.- Solitary waves.- Variance identity.- Symmetries and the lens transformation.- Stability of solitary waves.- The explicit critical singular peak-type solution.- The explicit critical singular ring-type solution.- The explicit supercritical singular peak-type solution.- Blowup rate, blowup profile, and power concentration.- The peak-type blowup profile.- Vortex solutions.- NLS on a bounded domain.- Derivation of reduced equations.- Loglog law and adiabatic collapse.- Singular H1 ring-type solutions.- Singular H1 vortex solutions.- Singular H1 peak-type solutions.- Singular standing-ring solutions.- Singular shrinking-ring solutions.- Critical and threshold powers for collapse.- Multiple filamentation.- Nonlinear Geometrical Optics (NGO) method.- Location of singularity.- Computation of solitary waves.- Numerical methods for the NLS.- Effects of spatial discretization.- Modulation theory.- Cubic-quintic and saturated nonlinearities.- Linear and nonlinear damping.- Nonparaxiality and backscattering (nonlinear Helmholtz equation).- Ultrashort pulses.- Normal and anomalous dispersion.- NGO method for ultrashort pulses with anomalous dispersion.- Continuations beyond the singularity.- Loss of phase and chaotic interactions.

Quantum Griffiths singularity of superconductor-metal transition in Ga thin films

Abstract: The Griffiths singularity in a phase transition, caused by disorder effects, was predicted more than 40 years ago. Its signature, the divergence of the dynamical critical exponent, is challenging to observe experimentally. We report the experimental observation of the quantum Griffiths singularity in a two-dimensional superconducting system. We measured the transport properties of atomically thin gallium films and found that the films undergo superconductor-metal transitions with increasing magnetic field. Approaching the zero-temperature quantum critical point, we observed divergence of the dynamical critical exponent, which is consistent with the Griffiths singularity behavior. We interpret the observed superconductor-metal quantum phase transition as the infinite-randomness critical point, where the properties of the system are controlled by rare large superconducting regions.

The 1965 Penrose singularity theorem

Abstract: We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful concept of the closed trapped surface was introduced. We include historical remarks, an appraisal of the theorem's impact, and relevant current and future work that belongs to its legacy.

Singular Bouncing Cosmology from Gauss-Bonnet Modified Gravity

Abstract: We study how a cosmological bounce with a Type IV singularity at the bouncing point, can be generated by a classical vacuum $F(G)$ gravity. We focus our investigation on the behavior of the vacuum $F(G)$ theory near the Type IV singular bouncing point and also we address the stability of the resulting solution, by treating the equations of motion as a dynamical system. In addition, we investigate how the scalar perturbations of the background metric evolve, emphasizing to cosmological times near the Type IV singular bouncing point. Finally, we also investigate which mimetic vacuum $F(G)$ gravity can describe the singular bounce cosmology.

Bouncing cosmology with future singularity from modified gravity

Abstract: We investigate which Jordan frame $F(R)$ gravity can describe a Type IV singular bouncing cosmological evolution, with special emphasis given near the point at which the Type IV singularity occurs. The cosmological bounce is chosen in such a way so that the bouncing point coincides exactly with Type IV singularity point. The stability of the resulting $F(R)$ gravity is examined and in addition, we study the Einstein frame scalar-tensor theory counterpart of the resulting Jordan frame $F(R)$ gravity. Also, by assuming that the Jordan frame metric is chosen in such a way so that, when conformally transformed in the Einstein frame, it yields a quasi de Sitter or de Sitter Friedmann-Robertson-Walker metric, we study the observational indexes which turn out to be consistent with Planck 2015 data in the case of the Einstein frame scalar theory. Finally, we study the behavior of the effective equation of state corresponding to the Type IV singular bounce and after we compare the resulting picture with other bouncing cosmologies, we critically discuss the implications of our analysis.

Finite-Time Stabilization for Vehicle Active Suspension Systems With Hard Constraints

Abstract: This paper presents the problem of finite-time stabilization for vehicle suspension systems with hard constraints based on terminal sliding-mode (TSM) control. As we know, one of the strong points of TSM control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. However, two main problems hindering the application of the TSM control are the singularity and chattering in TSM control systems. This paper proposes a novel second-order sliding-mode algorithm to soften the switching control law. The effect of the equivalent low-pass filter can be properly controlled in the algorithm based on requirements. Meantime, since the derivatives of term with fractional power do not appear in the control law, the control singularity is avoided. Thus, a chattering-free TSM control scheme for suspension systems is proposed, which allows both the chattering and singularity problems to be resolved. Finally, the effectiveness of the proposed approach is illustrated by both theoretical analysis and comparative experiment results.

The lifetime problem of evaporating black holes: Mutiny or resignation

Abstract: It is logically possible that regularly evaporating black holes (REBHs) exist in nature. In fact, the prevalent theoretical view is that these are indeed the real objects behind the curtain in astrophysical scenarios. There are several proposals for regularizing the classical singularity of black holes so that their formation and evaporation do not lead to information-loss problems. One characteristic is shared by most of these proposals: these REBHs present long-lived trapping horizons, with absolutely enormous evaporation lifetimes in whatever measure. Guided by the discomfort with these enormous and thus inaccessible lifetimes, we elaborate here on an alternative regularization of the classical singularity, previously proposed by the authors in an emergent gravity framework, which leads to a completely different scenario. In our scheme the collapse of a stellar object would result in a genuine time-symmetric bounce, which in geometrical terms amounts to the connection of a black-hole geometry with a white-hole geometry in a regular manner. The two most differential characteristics of this proposal are: (i) the complete bouncing geometry is a solution of standard classical general relativity everywhere except in a transient region that necessarily extends beyond the gravitational radius associated with the total mass of the collapsing object; and (ii) the duration of the bounce as seen by external observers is very brief (fractions of milliseconds for neutron-star-like collapses). This scenario motivates the search for new forms of stellar equilibrium different from black holes. In a brief epilogue we compare our proposal with a similar geometrical setting recently proposed by Haggard and Rovelli.

Resonant Dynamics and the Instability of Anti-de Sitter Spacetime.

Abstract: We consider spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant in five dimensions and analyze the evolution of small perturbations of anti-de Sitter (AdS) spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing the instability of AdS under arbitrarily small perturbations.

Categorical resolutions of irrational singularities

Abstract: We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived categories of smooth varieties. This provides a categorical resolution of the singularity.

On the effective metric of a Planck star

Abstract: Spacetime metrics describing ‘non-singular’ black holes are commonly studied in the literature as effective modification to the Schwarzschild solution that mimic quantum gravity effects removing the central singularity. Here we point out that to be physically plausible, such metrics should also incorporate the 1-loop quantum corrections to the Newton potential and a non-trivial time delay between an observer at infinity and an observer in the regular center. We present a modification of the well-known Hayward metric that features these two properties. We discuss bounds on the maximal time delay imposed by conditions on the curvature, and the consequences for the weak energy condition, in general violated by the large transversal pressures introduced by the time delay.

Particles approximations of Vlasov equations with singular forces : Propagation of chaos

Abstract: We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also provide results for forces with singularity up to $\alpha < d-1$ but with large enough cut-off. This last result thus almost includes the most interesting case of Coulombian or gravitational interaction, but it is also interesting when the strength of the singularity $\alpha$ is larger but close to one, in which case it allows for very small cut-off.

Nonsingular Black Holes in $f(R)$ Theories

Abstract: We study the structure of a family of static, spherically symmetric space-times generated by an anisotropic fluid and governed by a particular type of f(R) theory. We find that for a range of parameters with physical interest, such solutions represent black holes with the central singularity replaced by a finite size wormhole. We show that time-like geodesics and null geodesics with nonzero angular momentum never reach the wormhole throat due to an infinite potential barrier. For null radial geodesics, it takes an infinite affine time to reach the wormhole. This means that the resulting space-time is geodesically complete and, therefore, nonsingular despite the generic existence of curvature divergences at the wormhole throat.

Singular Inflationary Universe from $F(R)$ Gravity

Abstract: Unlike crushing singularities, the so-called Type IV finite-time singularity offers the possibility that the Universe passes smoothly through it, without any catastrophic effects. Then the question is if the effects of a Type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of $F(R)$ gravity. As we demonstrate, the effects of a Type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a Type IV singularity, with the singularity occurring at the end of inflation. Particularly we study a toy model and a singular version of the $R^2$ gravity Hubble rate. As we evince, some of the Hubble flow parameters become singular at the singularity, an effect which indicates that at that point a dynamical instability occurs. This dynamical instability eventually indicates the graceful exit from inflation. We demonstrate that the toy model has an unstable de Sitter point at the singularity, so indeed graceful exit could be triggered. In the case of the singular inflation model, graceful exit proceeds in the standard way. In the case of the singular inflation model, we found various scenarios for singular evolution, most of which are compatible with observations, and only one leads to severe instabilities. We also compare the ordinary Starobinsky with the singular inflation model, and we point out the qualitative and quantitative differences. Finally, we study the late-time dynamics of the toy model and of the singular inflation model and we demonstrate that the unification of early and late-time acceleration can be achieved. We also show that it is possible to achieve late-time acceleration similar to the $\Lambda$-Cold Dark Matter model.

Four loop renormalization of $\phi^3$ theory in six dimensions

Abstract: We renormalize six dimensional phi^3 theory in the modified minimal subtraction (MSbar) scheme at four loops. From the resulting beta-function, anomalous dimension and mass anomalous dimension we compute four loop critical exponents relevant to the Lee-Yang edge singularity and percolation problems. Using resummation methods and information on the exponents of the relevant two dimensional conformal field theory we obtain estimates for exponents in dimensions 3, 4and 5 which are in reasonable agreement with other techniques for these two problems. The renormalization group functions for the more general theory with an O(N) symmetry are also computed in order to obtain estimates of exponents at various fixed points in five dimensions. Included in this O(N) analysis is the full evaluation of the mass operator mixing matrix of anomalous dimensions at four loops. We show that its eigen-exponents are in agreement with the mass exponents computed at O(1/N^2) in the non-perturbative large N expansion.

Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies

Abstract: We present a comprehensive discussion of renormalisation of 3-point functions of scalar operators in conformal field theories in general dimension. We have previously shown that conformal symmetry uniquely determines the momentum-space 3-point functions in terms of certain integrals involving a product of three Bessel functions (triple-K integrals). The triple-K integrals diverge when the dimensions of operators satisfy certain relations and we discuss how to obtain renormalised 3-point functions in all cases. There are three different types of divergences: ultralocal, semilocal and nonlocal, and a given divergent triple-K integral may have any combination of them. Ultralocal divergences may be removed using local counterterms and this results in new conformal anomalies. Semilocal divergences may be removed by renormalising the sources, and this results in CFT correlators that satisfy Callan-Symanzik equations with beta functions. In the case of non-local divergences, it is the triple-K representation that is singular, not the 3-point function. Here, the CFT correlator is the coefficient of the leading nonlocal singularity, which satisfies all the expected conformal Ward identities. Such correlators exhibit enhanced symmetry: they are also invariant under dual conformal transformations where the momenta play the role of coordinates. When both anomalies and beta functions are present the correlators exhibit novel analytic structure containing products of logarithms of momenta. We illustrate our discussion with numerous examples, including free field realisations and AdS/CFT computations.

Regular rotating electrically charged black holes and solitons in non-linear electrodynamics minimally coupled to gravity

Abstract: In non-linear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have an obligatory de Sitter center. By the Gurses–Gursey algorithm they are transformed to spinning electrically charged solutions that are asymptotically Kerr–Newman for a distant observer. Rotation transforms the de Sitter center into a de Sitter vacuum surface which contains the equatorial disk r = 0 as a bridge. We present a general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the field equations. We find asymptotic solutions and show that de Sitter vacuum surfaces have properties of a perfect conductor and ideal diamagnetic, violation of the weak energy condition is prevented by the basic requirement of electrodynamics of continued media, and the Kerr ring singularity is replaced with the superconducting current.

Closed-Loop Inverse Kinematics for Redundant Robots: Comparative Assessment and Two Enhancements

Abstract: Motivated by the need of a robust and practical inverse kinematics (IK) algorithm for the WAM robot arm, we reviewed the most used closed-loop IK methods for redundant robots, analyzing their main points of concern: convergence, numerical error, singularity handling, joint limit avoidance, and the capability of reaching secondary goals. As a result of the experimental comparison, we propose two enhancements. The first is a new filter for the singular values of the Jacobian matrix that guarantees that its conditioning remains stable, while none of the filters found in the literature is successful at doing so. The second is to combine a continuous task priority strategy with selective damping to generate smoother trajectories. Experimentation on the WAM robot arm shows that these two enhancements yield an IK algorithm that improves on the reviewed state-of-the-art ones, in terms of the good compromise it achieves between time step length, Jacobian conditioning, multiple task performance, and computational time, thus constituting a very solid option in practice. This proposal is general and applicable to other redundant robots.

Logarithmic singularities and maximally supersymmetric amplitudes

Abstract: The dual formulation of planar N = 4 super-Yang-Mills scattering amplitudes makes manifest that the integrand has only logarithmic singularities and no poles at infinity. Recently, Arkani-Hamed, Bourjaily, Cachazo and Trnka conjectured the same singularity properties hold to all loop orders in the nonplanar sector as well. Here we conjecture that to all loop orders these constraints give us the key analytic information contained in dual conformal symmetry. We also conjecture that to all loop orders, while N = 8 supergravity has poles at infinity, at least at four points it has only logarithmic singularities at finite locations. We provide nontrivial evidence for these conjectures. For the three-loop four-point N = 4 super-Yang-Mills amplitude, we explicitly construct a complete basis of diagram integrands that has only logarithmic singularities and no poles at infinity. We then express the complete amplitude in terms of the basis diagrams, with the coefficients determined by unitarity. We also give examples at three loops showing how to make the logarithmic singularity properties manifest via dlog forms. We give additional evidence at four and five loops supporting the nonplanar logarithmic singularity conjecture. Furthermore, we present a variety of examples illustrating that these constraints are more restrictive than dual conformal symmetry. Our investigations show that the singularity structures of planar and nonplanar amplitudes in N = 4 super-Yang-Mills are strikingly similar. While it is not clear how to extend either dual conformal symmetry or a dual formulation to the nonplanar sector, these results suggest that related concepts might exist and await discovery. Finally, we describe the singularity structure of N = 8 supergravity at three loops and beyond.

R\'enyi entropy and conformal defects

Abstract: We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

Holographic Complexity And Cosmological Singularities

Abstract: We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.

Are We Approaching an Economic Singularity? Information Technology and the Future of Economic Growth

Abstract: What are the prospects for long-run economic growth?, the present study looks at a more recently launched hypothesis, which I label Singularity. The idea here is that rapid growth in computation and artificial intelligence will cross some boundary or Singularity after which economic growth will accelerate sharply as an ever-accelerating pace of improvements cascade through the economy. The paper develops a growth model that features Singularity and presents several tests of whether we are rapidly approaching Singularity. The key question for Singularity is the substitutability between information and conventional inputs. The tests suggest that the Singularity is not near.

Strings, branes and the self-dual solutions of Exceptional Field Theory

Abstract: It has been shown that membranes and fivebranes are wave-like or monopole-like solutions in some higher dimensional theory. Here the picture is completed by combining the wave and monopole solutions into a single solution of Exceptional Field Theory. This solution solves the twisted self-duality constraint. The 1/2 BPS brane spectrum, consisting of fundamental, solitonic and Dirichlet branes and their bound states, in ten- and eleven-dimensional supergravity may all be extracted from this single solution of Exceptional Field Theory. The solution’s properties such as its asymptotic behavior at the core and at infinity are investigated.

Singularity-free anisotropic strange quintessence star

Abstract: Present paper provides a new model of anisotropic strange star corresponding to the exterior Schwarzschild metric. The Einstein field equations have been solved by utilizing the Krori-Barua (KB) ansatz (Krori and Barua in J. Phys. A, Math. Gen. 8:508, 1975) in presence of quintessence field characterized by a parameter ω q with $-1<\omega_{q}<-\frac{1}{3}$ . The obtained solutions are free from central singularity. Our model is potentially stable. The numerical values of mass of the different strange stars SAXJ1808.4-3658(SS1) (radius=7.07 km), 4U1820-30 (radius=10 km), Vela X-12 (radius=9.99 km), PSR J 1614-2230 (radius=10.3 km) obtained from our model is very close to the observational data that confirms the validity of our proposed model. The interior solution is also matched to the exterior Schwarzschild spacetime in presence of thin shell where negative surface pressure is required to hold the thin shell against collapsing.