Showing papers on "Superpotential published in 2019"

dS Supergravity from 10d

Abstract: We consider flux compactification of type II string theory with local sources on SU(3)-structure manifolds. By adding pseudo-calibrated anti-$Dp$-branes wrapped on supersymmetric cycles we generalize all existing models so that the effective $d=4,$ ${\cal N}=1$ supergravity now includes a nilpotent multiplet. We present a new dictionary between string theory models and K{a}hler potential $K$ and superpotential $W$ for these dS supergravities with a nilpotent multiplet and non-linearly realized local supersymmetry. In addition to KKLT and LVS with uplifting $\overline{D3}$-branes, we have now new models with uplifting $\overline{D5}$, $\overline{D6}$, $\overline{D7}$, $\overline{D9}$-branes. The new uplifting contribution to the supergravity potential due to Volkov-Akulov supersymmetry is universal. As one application of our general result, we study classical flux compactifications of type IIA supergravity and find that a previously discovered universal tachyon is now absent.

dS vacua and the swampland

Abstract: In this note we revisit some of the recent 10d and 4d arguments suggesting that the uplifting of supersymmetric AdS vacua leads to a flattening of the potential, preventing the formation of dS vacua. We explain why the corresponding 10d approach is inconclusive and requires considerable modifications. We also show that while the flattening effects may occur for some extreme values of the parameters, they do not prevent the formation of dS vacua within the range of validity of the 4d KKLT models. The KL version of the KKLT scenario based on a racetrack superpotential requires parametrically small uplifting, which is not affected by flattening. We show that this scenario is compatible with the weak gravity conjecture for a broad choice of parameters of the KL model. Thus, the results of our analysis do not support the recent swampland conjecture.

A tale of exceptional 3 d dualities

Abstract: We consider interesting Seiberg dualities for Usp gauge theories with an antisymmetric, 8 fundamentals and no superpotential. We reduce to three dimensions and systematically analyze deformations triggered by real and complex masses, reaching a plethora of $$ \mathcal{N} $$ = 2 dualities for U(N) and Usp(2N) gauge theories, possibly with monopole superpotentials and Chern-Simons interactions. Special cases of these “exceptional dualities” are: supersymmetry enhancement dualities, “duality appetizers” and many known dualities relating rank-1 gauge groups. The 4d $$ \mathcal{N} $$ = 1 Usp dualities provide a unified perspective on many curious phenomena of 3d and 4d gauge theories with four supercharges. Finally, we propose a free mirror for A2N Argyres-Douglas, with its related adjoint-Usp(2N) duality, and we construct a mirror for adjoint-U(N), with an arbitrary number flavors and zero superpotential.

A General Classification of Starobinsky-like Inflationary Avatars of SU(2,1)/SU(2)×U(1) No-Scale Supergravity

Abstract: Measurements of the cosmic microwave background (CMB) favour models of inflation with a small tensor-to-scalar ratio r, as predicted by the Starobinsky R + R2 model. It has been shown previously that various models based on no-scale supergravity with different forms of superpotential make predictions similar to those of the Starobinsky model. In this paper we present a unified and general treatment of Starobinsky avatars of no-scale supergravity, using the underlying non-compact SU(2,1)/SU(2)×U(1) symmetry to demonstrate equivalences between different models, exhibiting 6 specific equivalence classes.

Large N renormalization group flows in 3d \( \mathcal{N} \) = 1 Chern-Simons-Matter theories

Abstract: We discuss 3d $$ \mathcal{N} $$ = 1 supersymmetric SU(N) and U(N) Chern-Simons-matter theories, with Nf matter superfields in the fundamental representation of SU(N) or U(N). In the large N ’t Hooft limit with fixed ’t Hooft coupling λ these theories have one (for Nf = 1) or two (for Nf> 1) exactly marginal deformations in the superpotential. At finite N these couplings acquire a beta function. We compute the beta function exactly for λ = 0, at leading order in 1/N. For Nf = 1 we find four fixed points, one of which is triply-degenerate. We show that at large N there are at most six fixed points for any λ, and conjecture that there are exactly six, with three of them stable (including a point with enhanced $$ \mathcal{N} $$ = 2 supersymmetry). The strong-weak coupling dualities of $$ \mathcal{N} $$ = 1 Chern-Simons-matter theories map each of these fixed points to a dual one. We show that at large N the phase structure near each of the three stable fixed points is different. For Nf> 1 we analyze the fixed points at weak coupling, and we work out the action of the strong-weak coupling duality on the marginal and relevant superpotential couplings at large N (which was previously known only for Nf = 1). In addition, we compute in these theories the 2-point and 3-point functions of the lowest gauge-invariant singlet superfield at large N, for all values of λ and of the superpotential couplings, and use them to test the large N dualities. This computation is one of the ingredients needed for a computation of the beta function at order 1/N for all λ, which we leave for future work. We also discuss Chern-Simons-matter theories with extra Hubbard-Stratonovich type singlet fields, and suggest dualities between them.

Integer superspin supercurrents of matter supermultiplets

Abstract: In recent papers [18, 21] we demonstrated that consistent and non-trivial linear transformations of matter supermultiplets generate half-integer superspin supercurrents and the cubic interactions between matter and half-integer superspin supermultiplets. In this work we show that consistent and non-trivial antilinear transformations of matter superfields lead to the construction of integer superspin supercurrents and the cubic interactions between mater and integer superspin supermultiplets. Applying Noether’s method to these transformations, we find new integer superspin supercurrents for the case of a free massless chiral superfield. Furthermore, we use them to find new integer superspin supercurrent multiplets for a massive chiral superfield and a chiral superfield with a linear superpotential. Also various selection rules for such interactions are found.

A new N=1 AdS4 Vacuum of Maximal Supergravity

Abstract: The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N=8, SO(8) gauged supergravity using Machine Learning software has led to a discovery of a new N=1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3)xZ2-invariant truncation of the N=8 theory to an N=1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the N=1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3)xZ2-invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional Z2^3-invariant scalar manifold (SU(1,1)/U(1))^7, for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new N=1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an N=1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.

Superpotential method for chiral cosmological models connected with modified gravity

Abstract: We consider chiral cosmological models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an $f(R)$ gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the quasi-steady-state (QSS) model, with the aim of constructing single- and double-field potentials for one and the same behavior of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model.

Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor

Abstract: We derive a superpotential for null electromagnetic fields in which the field line structure is in the form of an arbitrary torus knot. These fields are shown to correspond to single copies of a class of anti-self-dual Kerr-Schild spacetimes containing the Sparling-Tod metric. This metric is the pure Weyl double copy of the electromagnetic Hopfion, and we show that the Eguchi-Hanson metric is a mixed Weyl double copy of this Hopfion and its conformally inverted state. We formulate two conditions for electromagnetic fields, generalizing torus knotted fields and linked optical vortices, that, via the zero rest mass equation for spin 1 and spin 2, defines solutions of linearized Einstein’s equation possessing a Hopf fibration as the curves along which no stretching, compression or precession will occur. We report on numerical findings relating the stability of the linked and knotted zeros of the Weyl tensor and their relation to linked optical vortices.

Type IIA flux vacua with mobile D6-branes

Abstract: We analyse type IIA Calabi-Yau orientifolds with background fluxes and D6-branes. The presence of D6-brane deformation moduli redefines the 4d dilaton and complex structure fields and complicates the analysis of such vacua in terms of the effective Kahler potential and superpotential. One may however formulate the F-term scalar potential as a bilinear form on the flux-axion polynomials ρA invariant under the discrete shift symmetries of the 4d effective theory. We express the conditions for Minkoswki and AdS flux vacua in terms of such polynomials, which allow to extend the analysis to include vacua with mobile D6-branes. We find a new, more general class of $$ \mathcal{N}=0 $$ Minkowski vacua, which nevertheless present a fairly simple structure of (contravariant) F-terms. We compute the soft-term spectrum for chiral models of intersecting D6-branes in such vacua, finding a quite universal pattern.

Precise prediction for the W boson mass in the MRSSM

Abstract: The mass of the W boson, MW, plays a central role for high-precision tests of the electroweak theory. Confronting precise theoretical predictions with the accurately measured experimental value provides a high sensitivity to quantum effects of the theory entering via loop contributions. The currently most accurate prediction for the W boson mass in the Minimal R-symmetric Supersymmetric Standard Model (MRSSM) is presented. Employing the on-shell scheme, it combines all numerically relevant contributions that are known in the Standard Model (SM) in a consistent way with all MRSSM one-loop corrections. Special care is taken in the treatment of the triplet scalar vacuum expectation value vT that enters the prediction for MW already at lowest order. In the numerical analysis the decoupling properties of the supersymmetric loop contributions and the comparison with the MSSM are investigated. Potentially large numerical effects of the MRSSM-specific Λ superpotential couplings are highlighted. The comparison with existing results in the literature is discussed.

Relative quantum cohomology

Abstract: We establish a system of PDE, called open WDVV, that constrains the bulk-deformed superpotential and associated open Gromov-Witten invariants of a Lagrangian submanifold $L \subset X$ with a bounding chain. Simultaneously, we define the quantum cohomology algebra of $X$ relative to $L$ and prove its associativity. We also define the relative quantum connection and prove it is flat. A wall-crossing formula is derived that allows the interchange of point-like boundary constraints and certain interior constraints in open Gromov-Witten invariants. Another result is a vanishing theorem for open Gromov-Witten invariants of homologically non-trivial Lagrangians with more than one point-like boundary constraint. In this case, the open Gromov-Witten invariants with one point-like boundary constraint are shown to recover certain closed invariants. From open WDVV and the wall-crossing formula, a system of recursive relations is derived that entirely determines the open Gromov-Witten invariants of $(X,L) = (\mathbb{C}P^n, \mathbb{R}P^n)$ with $n$ odd, defined in previous work of the authors. Thus, we obtain explicit formulas for enumerative invariants defined using the Fukaya-Oh-Ohta-Ono theory of bounding chains.

On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories

Abstract: Recently, it was found that certain 4d $$ \mathcal{N}=1 $$ Lagrangians experience supersymmetry enhancement at their IR fixed point, thereby giving a Lagrangian description for a plethora of Argyres-Douglas theories. A generic feature of these Lagrangians is that a number of gauge invariant operators decouple (as free fields) along the RG-flow. These decoupled operators can be naturally taken into account from the beginning itself by introducing additional gauge singlets (sometimes called “flipping fields”) that couple to the decoupled operators via appropriate superpotential terms. It has also been checked that upon dimensionally reducing to 3d, the (A1, A2n−1) type Lagrangians only produce the expected behavior when flipping fields are included in the Lagrangian. In this paper we further investigate the role of flipping fields and find an example where the expected necessity of including the flipping fields in the dimensionally reduced Lagrangians seems to get violated. In the process we find two new dual Lagrangians for the so called 3d T [SU(2)] theory.

U ( 1 ) R inspired inflation model in no-scale supergravity

Abstract: We consider a cosmological inflation scenario based on a no-scale supergravity sector with $U(1{)}_{R}$ symmetry. It is shown that a tree level $U(1{)}_{R}$ symmetric superpotential alone does not lead to a slowly rolling scalar potential. A deformation of this tree level superpotential by including an explicit $R$ symmetry breaking term beyond the renormalizable level is proposed. The resulting potential is found to be similar (but not exactly the same) to the one in the Starobinsky inflation model. We emphasize that for successful inflation, with the scalar spectral index ${n}_{s}\ensuremath{\sim}0.96$ and the tensor-to-scalar ratio $rl0.08$, a correlation between the mass parameters in the superpotential and the vacuum expectation value of the modulus field $T$ in the K\"ahler potential must be adopted.

From Minkowski to de Sitter in multifield no-scale models

Abstract: We show the uniqueness of superpotentials leading to Minkowski vacua of single-field no-scale supergravity models, and the construction of dS/AdS solutions using pairs of these single-field Minkowski superpotentials. We then extend the construction to two- and multifield no-scale supergravity models, providing also a geometrical interpretation. We also consider scenarios with additional twisted or untwisted moduli fields, and discuss how inflationary models can be constructed in this framework.

Beta function quintessence cosmological parameters and fundamental constants – II. Exponential and logarithmic dark energy potentials

Abstract: This paper uses the beta function formalism to extend the analysis of quintessence cosmological parameters to the logarithmic and exponential dark energy potentials. The previous paper (Thompson 2018) demonstrated the formalism using power and inverse power potentials. The essentially identical evolution of the Hubble parameter for all of the quintessence cases and LambdaCDM is attributed to the flatness of the quintessence dark energy potentials in the dark energy dominated era. The Hubble parameter is therefore incapable of discriminating between static and dynamic dark energy. Unlike the other three potentials considered in the two papers the logarithmic dark energy potential requires a numerical integration in the formula for the superpotential rather than being an analytic function. The dark energy equation of state and the fundamental constants continue to be good discriminators between static and dynamical dark energy. A new analysis of quintessence with all four of the potentials relative the swampland conjectures indicates that the conjecture on the change in the scalar field is satisfied but that the conjecture on the change of the potential is not.

Mirror symmetry for the Landau–Ginzburg A-model M=Cn, W=z1?zn

Abstract: We calculate the category of branes in the Landau–Ginzburg A-model with background M=Cn and superpotential W=z1⋯zn in the form of microlocal sheaves along a natural Lagrangian skeleton. Our arguments employ the framework of perverse schobers, and our results confirm expectations from mirror symmetry.

Graded quivers and B-branes at Calabi-Yau singularities

Abstract: A graded quiver with superpotential is a quiver whose arrows are assigned degrees c ∈ {0, 1, ⋯ , m}, for some integer m ≥ 0, with relations generated by a superpotential of degree m − 1. Ordinary quivers (m = 1) often describe the open string sector of D-brane systems; in particular, they capture the physics of D3-branes at local Calabi-Yau (CY) 3-fold singularities in type IIB string theory, in the guise of 4d $$ \mathcal{N} $$ = 1 supersymmetric quiver gauge theories. It was pointed out recently that graded quivers with m = 2 and m=3 similarly describe systems of D-branes at CY 4-fold and 5-fold singularities, as 2d $$ \mathcal{N} $$ = (0, 2) and 0d $$ \mathcal{N} $$ = 1 gauge theories, respectively. In this work, we further explore the correspondence between m-graded quivers with superpotential, Q(m), and CY (m + 2)-fold singularities, Xm+2. For any m, the open string sector of the topological B-model on Xm+2 can be described in terms of a graded quiver. We illustrate this correspondence explicitly with a few infinite families of toric singularities indexed by m ∈ ℕ, for which we derive “toric” graded quivers associated to the geometry, using several complementary perspectives. Many interesting aspects of supersymmetric quiver gauge theories can be formally extended to any m; for instance, for one family of singularities, dubbed C(Y1,0(ℙm)), that generalizes the conifold singularity to m > 1, we point out the existence of a formal “duality cascade” for the corresponding graded quivers.

Construction of solvable non-central potential using vector superpotential: a new approach

Abstract: We introduce here vector superpotential which is useful to find general potential form using supersymmetric quantum mechanics (SUSY QM) approach. Using the vector superpotential, we reconstruct different solved central potentials and non-central shape variant or shape invariant potentials. To construct and reconstruct the central potentials and non-central potentials, appropriate choice of radial part of the superpotential as well as angular and azimuthal parts of the superpotential is required. Our main aim is to construct angular and azimuthal parts of potential directly from the appropriate choice of vector superpotential. We have reconstructed few potentials which are solved by different researchers using different methods of solution and also constructed new non-central potentials.

dS Vacua and the Swampland.

Abstract: In this note we revisit some of the recent 10d and 4d arguments suggesting that uplifting of supersymmetric AdS vacua leads to flattening of the potential, preventing formation of dS vacua. We explain why the corresponding 10d approach is inconclusive and requires considerable modifications. We also show that while the flattening effects may occur for some extreme values of the parameters, they do not prevent the formation of dS vacua within the range of validity of the 4d KKLT models. The KL version of the KKLT scenario based on a racetrack superpotential requires parametrically small uplifting, which is not affected by flattening. We show that this scenario is compatible with the weak gravity conjecture for a broad choice of parameters of the KL model. Thus, the results of our analysis do not support the recent swampland conjecture.

Dualities for adjoint SQCD in three dimensions and emergent symmetries

Abstract: In this paper we study dualities for $$ \mathcal{N} $$ = 2 gauge theories in three dimensions with matter in the fundamental and adjoint representation. The duality we propose, analogous to mirror symmetry, is obtained starting from $$ \mathcal{N} $$ = 4 mirror theories and turning on a certain superpotential deformation involving monopole operators. We study the role of emergent symmetries in the dual theory, focusing on the case of models with gauge symmetry U(2) or SU(2). We find that SU(2) adjoint SQCD with one flavor and zero superpotential is dual to SQED with two flavors and three singlets. As a byproduct, we recover several dualities for theories with $$ \mathcal{N} $$ = 2 and $$ \mathcal{N} $$ = 4 supersymmetry, including the duality appetizer of Jafferis and Yin.

Exploring the Landscape of effective field theories

Abstract: In this thesis we provide new tools to determine and explore the Landscape of four-dimensional effective field theories originating from string and M-theory. The main aim is to introduce, within four-dimensional effective descriptions, elements that are predicted from string theory. To this end, a hierarchy of forms is introduced within the four-dimensionalN=1 supergravity theories. The inclusion of gauge three-forms delivers a dynamical way to generate flux-induced superpotentials. Instead, gauge two-forms, dual descriptions of axions, may be eventually gauged by three-forms to generate a superpotential coupling between the different chiral multiplet sectors of the theory. The mutual constraints among the background fluxes, such as tadpole cancellations, are imposed by gauge four-forms. A hierarchy of objects, to which the gauge forms couple, is then introduced: four-dimensional BPS-strings, membranes and 3-branes enlarge the Landscape, allowing the background fluxes to consistently change transversing different spacetime regions. The Freed-Witten anomaly cancellations and the changing of tadpole cancellation conditions due to background sources are neatly expressed by BPS-junctions of membranes ending on strings and 3-branes ending on membranes. Membrane-mediated domain wall transitions are studied, which determine how the scalar fields flow connecting a vacuum to another of the Landscape. According to the perturbative regime that is scanned only some transitions are allowed, with a dramatic influence on the spectrum of objects that can be consistently incorporated in the four-dimensional description.

Precise prediction for the W boson mass in the MRSSM

Abstract: The mass of the W boson, $M_W$, plays a central role for high-precision tests of the electroweak theory. Confronting precise theoretical predictions with the accurately measured experimental value provides a high sensitivity to quantum effects of the theory entering via loop contributions. The currently most accurate prediction for the W boson mass in the Minimal R-symmetric Supersymmetric Standard Model (MRSSM) is presented. Employing the on-shell scheme, it combines all numerically relevant contributions that are known in the Standard Model (SM) in a consistent way with all MRSSM one-loop corrections. Special care is taken in the treatment of the triplet scalar vacuum expectation value $v_T$ that enters the prediction for $M_W$ already at lowest order. In the numerical analysis the decoupling properties of the supersymmetric loop contributions and the comparison with the MSSM are investigated. Potentially large numerical effects of the MRSSM-specific $\Lambda$ superpotential couplings are highlighted. The comparison with existing results in the literature is discussed.

Holomorphic Structure and Quantum Critical Points in Supersymmetric Lifshitz Field Theories

Abstract: We construct supersymmetric Lifshitz field theories with four real supercharges in a general number of space dimensions. The theories consist of complex bosons and fermions and exhibit a holomorphic structure and non-renormalization properties of the superpotential. We study the theories in a diverse number of space dimensions and for various choices of marginal interactions. We show that there are lines of quantum critical points with an exact Lifshitz scale invariance and a dynamical critical exponent that depends on the coupling constants.

Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor

Abstract: We derive a superpotential for null electromagnetic fields in which the field line structure is in the form of an arbitrary torus knot. These fields are shown to correspond to single copies of a class of anti-self-dual Kerr-Schild spacetimes containing the Sparling-Tod metric. This metric is the pure Weyl double copy of the electromagnetic Hopfion, and we show that the Eguchi-Hanson metric is a mixed Weyl double copy of this Hopfion and its conformally inverted state. We formulate two conditions for electromagnetic fields, generalizing torus knotted fields and linked optical vortices, that, via the zero rest mass equation for spin 1 and spin 2, defines solutions of linearized Einstein's equation possessing a Hopf fibration as the curves along which no stretching, compression or precession will occur. We report on numerical findings relating the stability of the linked and knotted zeros of the Weyl tensor and their relation to linked optical vortices.

Twisted characters and holomorphic symmetries

Abstract: We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly as a family over the space of nilpotent supercharges in minimal supersymmetry. The BV formalism allows one to work with or without auxiliary fields, according to preference; for chiral superfields, we show that the result of the twist is an identical BV theory, the holomorphic $\beta\gamma$ system with superpotential, independent of whether or not auxiliary fields are included. We compute the character of local operators in this holomorphic theory, demonstrating agreement of the free local operators with the usual index of free fields. The local operators with superpotential are computed via a spectral sequence, and are shown to agree with functions on a formal mapping space into the derived critical locus of the superpotential. We consider the holomorphic theory on various geometries, including Hopf manifolds and products of arbitrary pairs of Riemann surfaces, and offer some general remarks on dimensional reductions of holomorphic theories along the $(n-1)$-sphere to topological quantum mechanics. We also study an infinite-dimensional enhancement of the flavor symmetry in this example, to a recently-studied central extension of the derived holomorphic functions with values in the original Lie algebra that generalizes the familiar Kac--Moody enhancement in two-dimensional chiral theories.

Heterotic backgrounds via generalised geometry: moment maps and moduli

Abstract: We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within $O(6,6+n)\times\mathbb{R}^+$ generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the Kahler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.