Showing papers on "Superpotential published in 2018"

The type IIA flux potential, 4-forms and Freed-Witten anomalies

Abstract: We compute the full classical 4d scalar potential of type IIA Calabi-Yau orientifolds in the presence of fluxes and D6-branes. We show that it can be written as a bilinear form V = ZABρAρB, where the ρA are in one-to-one correspondence with the 4-form fluxes of the 4d effective theory. The ρA only depend on the internal fluxes, the axions and the topological data of the compactification, and are fully determined by the Freed-Witten anomalies of branes that appear as 4d string defects. The quadratic form ZAB only depends on the saxionic partners of these axions. In general, the ρA can be seen as the basic invariants under the discrete shift symmetries of the 4d effective theory, and therefore the building blocks of any flux-dependent quantity. All these polynomials may be obtained by derivation from one of them, associated to a universal 4-form. The standard $$ \mathcal{N}=1 $$ supergravity flux superpotential is uniquely determined from this master polynomial, and vice versa.

Decoding a three-dimensional conformal manifold

Abstract: We study the one-dimensional complex conformal manifold that controls the infrared dynamics of a three-dimensional $$ \mathcal{N} $$ = 2 supersymmetric theory of three chiral superfields with a cubic superpotential. Two special points on this conformal manifold are the well-known XYZ model and three decoupled copies of the critical Wess-Zumino model. The conformal manifold enjoys a discrete duality group isomorphic to S4 and can be thought of as an orbifold of CP1. We use the 4 − e expansion and the numerical conformal bootstrap to calculate the spectrum of conformal dimensions of low-lying operators and their OPE coefficients, and find a very good quantitative agreement between the two approaches.

$\mathcal{N}{=}1$ dualities in 2+1 dimensions

Abstract: We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared SU(N) ↔ U(k) duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the e-expansion.

A universal tachyon in nearly no-scale de Sitter compactifications

Abstract: We investigate de Sitter solutions of $$ \mathcal{N}=1 $$ supergravity with an F-term scalar potential near a no-scale Minkowski point, as they may in particular arise from flux compactifications in string theory. We show that a large class of such solutions has a universal tachyon with $$ \eta \le -\frac{4}{3} $$ at positive vacuum energies, thus forbidding meta-stable de Sitter vacua and slow-roll inflation. The tachyon aligns with the sgoldstino in the Minkowski limit, whereas the sgoldstino itself is generically stable in the de Sitter vacuum due to mass mixing effects. We specify necessary conditions for the superpotential and the Kahler potential to avoid the instability. Our result may also help to explain why the program of classical de Sitter hunting has remained unsuccessful, while constructions involving instantons or non-geometric fluxes have led to various examples of meta-stable de Sitter vacua.

Opers, surface defects, and Yang-Yang functional

Abstract: We explore the non-perturbative Dyson-Schwinger equations obeyed by the partition functions of the $\Omega$-deformed $\mathcal{N}=2, d=4$ supersymmetric linear quiver gauge theories in the presence of surface defects. We demonstrate that the partition functions of different types of defects (orbifold or vortex strings) are related by analytic continuation. We introduce Darboux coordinates on a patch of the moduli space of flat $SL(N)$-connections on a sphere with special punctures, which generalize the NRS coordinates defined in the $SL(2)$ case. Finally, we compare the generating function of the Lagrangian variety of opers in these Darboux coordinates with the effective twisted superpotential of the linear quiver theory in the two-dimensional $\Omega$-background, thereby proving the NRS conjecture and its generalization to the $SL(3)$ case.

Three-forms, dualities and membranes in four-dimensional supergravity

Abstract: We consider four-dimensional $$ \mathcal{N}=1 $$ supergravity models of a kind appearing in string flux compactifications. It has been recently shown that, by using double three-form multiplets instead of ordinary chiral multiplets, one can promote to dynamical variables (part of) the quantized numbers appearing in the flux-induced superpotential. We show that double three-form multiplets naturally transform under symplectic dualities associated with the special Kahler structure that characterizes their scalar sector. Furthermore, we discuss how to couple membranes which carry arbitrary ‘electric-magnetic’ charges. The complete action is supersymmetric, kappa-symmetric and duality covariant. As an application, we derive the flow equations for BPS domain walls sourced by membranes and give simple analytic examples of their solution.

Infinitely many M2-instanton corrections to M-theory on G(2)-manifolds

Abstract: We consider the non-perturbative superpotential for a class of four-dimensional $$ \mathcal{N}=1 $$ vacua obtained from M-theory on seven-manifolds with holonomy G2. The class of G2-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over S3. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of [1], which relates M-theory on TCS G2-manifolds to E8 × E8 heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the G2-compactification.

N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries.

Abstract: We consider three-dimensional sQED with 2 flavors and minimal supersymmetry. We discuss various models which are dual to Gross-Neveu-Yukawa theories. The $U(2)$ ultraviolet global symmetry is often enhanced in the infrared, for instance to $O(4)$ or $SU(3)$. This is analogous to the conjectured behaviour of non-supersymmetric QED with 2 flavors. A perturbative analysis of the Gross-Neveu-Yukawa models in the $D = 4 - \varepsilon$ expansion shows that the $U(2)$ preserving superpotential deformations of the sQED (modulo tuning mass terms to zero) are irrelevant, so the fixed points with enhanced symmetry are stable. We also construct an example of $\mathcal{N} = 2$ sQED with 4 flavors that exhibits enhanced $SO(6)$ symmetry.

Dualities and Phases of $3D N=1$ SQCD

Abstract: We study gauge theories with $$ \mathcal{N}=1 $$ supersymmetry in 2+1 dimensions. We start by calculating the 1-loop effective superpotential for matter in an arbitrary representation. We then restrict ourselves to gauge theories with fundamental matter. Using the 1-loop superpotential, we find a universal form for the phase diagrams of many such gauge theories, which is proven to persist to all orders in perturbation theory using a symmetry argument. This allows us to conjecture new dualities for $$ \mathcal{N}=1 $$ gauge theories with fundamental matter. We also show that these dualities are related to results in $$ \mathcal{N}=2 $$ supersymmetric gauge theories, which provides further evidence for them.

The method of generating functions in exact scalar field inflationary cosmology

Abstract: The construction of exact solutions in scalar field inflationary cosmology is of growing interest. In this work, we review the results which have been obtained with the help of one of the most effective methods, viz., the method of generating functions for the construction of exact solutions in scalar field cosmology. We also include in the debate the superpotential method, which may be considered as the bridge to the slow roll approximation equations. Based on the review, we suggest a classification for the generating functions, and find a connection for all of them with the superpotential.

De Sitter vacua in no-scale supergravity

Abstract: No-scale supergravity is the appropriate general framework for low-energy effective field theories derived from string theory. The simplest no-scale Kahler potential with a single chiral field corresponds to a compactification to flat Minkowski space with a single volume modulus, but generalizations to single-field no-scale models with de Sitter vacua are also known. In this paper we generalize these de Sitter constructions to two- and multi-field models of the types occurring in string compactifications with more than one relevant modulus. We discuss the conditions for stability of the de Sitter solutions and holomorphy of the superpotential, and give examples whose superpotential contains only integer powers of the chiral fields.

A tale of exceptional 3d 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 $A_{2N}$ 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.

Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds

Abstract: We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S^3$. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of arXiv:1708.07215, which relates M-theory on TCS $G_2$-manifolds to $E_8\times E_8$ heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the $G_2$-compactification.

A General Classification of Starobinsky-like Inflationary Avatars of SU(2,1)/SU(2) x 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 + R^2 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) x U(1) symmetry to demonstrate equivalences between different models, exhibiting 6 specific equivalence classes.

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.

De Sitter Vacua in No-Scale Supergravity

Abstract: No-scale supergravity is the appropriate general framework for low-energy effective field theories derived from string theory. The simplest no-scale Kahler potential with a single chiral field corresponds to a compactification to flat Minkowski space with a single volume modulus, but generalizations to single-field no-scale models with de Sitter vacua are also known. In this paper we generalize these de Sitter constructions to two- and multi-field models of the types occurring in string compactifications with more than one relevant modulus. We discuss the conditions for stability of the de Sitter solutions and holomorphy of the superpotential, and give examples whose superpotential contains only integer powers of the chiral fields.

Mirror theories of 3d $\mathcal{N}=2$ SQCD

Abstract: Using a recently proposed duality for U(N ) supersymmetric QCD (SQCD) in three dimensions with monopole superpotential, in this paper we derive the mirror dual description of $$ \mathcal{N} $$ = 2 SQCD with unitary gauge group, generalizing the known mirror dual description of abelian gauge theories We match the chiral ring of the dual theories and their partition functions on the squashed sphere We also conjecture a generalization for SQCD with orthogonal and symplectic gauge groups

SUSY enhancement from T-branes

Abstract: We use the F-theoretic engineering of four-dimensional rank-one superconformal field theories to provide a geometric understanding of the phenomenon of supersymmetry enhancement along the RG flow, recently observed by Maruyoshi and Song. In this context, the superpotential deformations responsible for such flows are interpreted as T-brane backgrounds and encoded in the geometry of elliptically-fibered fourfolds. We formulate a simple algebraic criterion to select all supersymmetry-enhancing flows and, without any maximization process, derive the main features of the corresponding $$ \mathcal{N} $$ = 2 theories in the infrared.

Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an L∞ algebra

Abstract: We consider finite deformations of the Hull-Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric vacuum leads to a thirdorder Maurer-Cartan equation that controls the moduli. The resulting complex effective action generalises that of both Kodaira-Spencer and holomorphic Chern-Simons theory. The supersymmetric locus of this action is described by an L3 algebra.

Liberated N=1 Supergravity

Abstract: We discuss a new interaction for chiral models in four-dimensional ${\cal N}=1$ supergavity. It contains a new arbitrary function in addition to the Kahler potential and superpotential. Its features include linearly realized off-shell supersymmetry, Kahler-Weyl invariance and broken supersymmetry. The corresponding scalar potential is augmented by the arbitrary function which allows freedom in constructing low-energy phenomenological models and inflationary models rooted in supergravity.

Between Symmetry and Duality in Supersymmetric Quantum Field Theories.

Abstract: We study two cases of interrelations between the enhancement of symmetries in the infrared (IR) and duality properties of supersymmetric quantum field theories in four dimensions. First, we discuss an SU(2) N=1 model with four flavors, singlet fields, and a superpotential. We show that this model flows to a conformal field theory with E_{6}×U(1) global symmetry. The enhancement of the flavor symmetry follows from Seiberg duality. The second example is concerned with an SU(4) gauge theory with matter in the fundamental and antisymmetric representations. We argue that this model has enhanced SO(12) symmetry in the IR, and, guided by this enhancement, we deduce a new IR duality.

Three-forms, dualities and membranes in four-dimensional supergravity

Abstract: We consider four-dimensional $\mathcal{N}=1$ supergravity models of a kind appearing in string flux compactifications. It has been recently shown that, by using double three-form multiplets instead of ordinary chiral multiplets, one can promote to dynamical variables (part of) the quantized numbers appearing in the flux-induced superpotential. We show that double three-form multiplets naturally transform under symplectic dualities associated with the special Kahler structure that characterizes their scalar sector. Furthermore, we discuss how to couple membranes which carry arbitrary `electric-magnetic' charges. The complete action is supersymmetric, kappa-symmetric and duality covariant. As an application, we derive the flow equations for BPS domain walls sourced by membranes and give simple analytic examples of their solution.

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

Abstract: We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kahler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kahler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

On 3d Seiberg-Like Dualities with Two Adjoints

Abstract: We study $N = 2$ 3-d theories with two adjoints and fundamental flavors along with D-type superpotential. For superpotential $W_{D_{n+2}} = \mathrm{Tr} \left(X^{n+1}+X Y^2\right)$ with $n$ odd, we propose the 3d dualities, which we motivate from the dimensional reduction of the related 4-d theory. We consider the factorization of the superconformal index and match precisely the vortex partition function of the dual pairs. In the language of the Higgs branch localization, the nonzero contribution of the vortex partition function comes from the discrete Higgs vacua of the massively deformed theory, which precisely matches with that of the dual theory. We also clarify the monopole operators parametrizing the Coulomb branch of such theories. Existence of independent monopole operators of charge 2 is crucial to describe the Coulomb branch.

On multi-field flows in gravity and holography

Abstract: We perform a systematic analysis of flow-like solutions in theories of Einstein gravity coupled to multiple scalar fields, which arise as holographic RG flows as well as in the context of cosmological solutions driven by scalars. We use the first order formalism and the superpotential formulation to classify solutions close to generic extrema of the scalar potential, and close to “bounces,” where the flow is inverted in some or all directions and the superpotential becomes multi-valued. Although the superpotential formulation contains a large redundancy, we show how this can be completely lift by suitable regularity conditions. We place the first order formalism in the context of Hamilton-Jacobi theory, where we discuss the possibility of non-gradient flows and their connection to non-separable solutions of the Hamilton-Jacobi equation. We argue that non-gradient flows may be useful in the presence of global symmetries in the scalar sector.

Bands and gaps in Nekrasov partition function

Abstract: We discuss the effective twisted superpotentials of 2d $$ \mathcal{N} $$ = (2, 2) theories arising upon the reduction of 4d $$ \mathcal{N} $$ = 2 gauge theories on the Ω-deformed cigar-like geometry. We explain field-theoretic origins of the gaps in the spectrum in the corresponding quantum mechanical (QM) systems. We find local 2d descriptions of the physics near these gaps by resumming the non-perturbative part of the twisted superpotential and discuss arising wall-crossing phenomena. The interpretation of the associated phenomena in the classical Liouville theory and in the scattering of two heavy states in AdS3 gravity is suggested. Some comments concerning a possible interpretation of the band structure in QM in terms of the Schwinger monopole-pair production in 4d are presented.

Surface operators in 5d gauge theories and duality relations

Abstract: We study half-BPS surface operators in 5d $$ \mathcal{N} $$ = 1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations, we obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.

Dualities and Phases of 3D N=1 SQCD

Abstract: We study gauge theories with N=1 supersymmetry in 2+1 dimensions. We start by calculating the 1-loop effective superpotential for matter in an arbitrary representation. We then restrict ourselves to gauge theories with fundamental matter. Using the 1-loop superpotential, we find a universal form for the phase diagrams of many such gauge theories, which is proven to persist to all orders in perturbation theory using a symmetry argument. This allows us to conjecture new dualities for N=1 gauge theories with fundamental matter. We also show that these dualities are related to results in N=2 supersymmetric gauge theories, which provides further evidence for them.

Supersymmetric integrable theories without particle production

Abstract: We consider a theory of scalar superfields in two dimensions with arbitrary superpotential. By imposing no particle production in tree level scattering, we constrain the form of the admissible interactions, recovering a supersymmetric extension of the sinh-Gordon model.

Distinguishing charged Higgs bosons from different representations at the LHC

Abstract: Extending the Standard Model (SM) scalar sector via the addition of one or more Higgs fields in higher dimensional representations adds one or more charged Higgs bosons to the spectrum. Some of these gauge representations with appropriate hypercharge contain doubly-charged Higgs bosons and can be easily distinguished from the models that contain only singly-charged Higgs bosons. In this study we focus on the more challenging question of distinguishing singly-charged Higgs bosons from different representations, viz. doublets and triplets of the SU(2) L gauge group. We consider a supersymmetric extension of the SM with a gauge singlet and an SU(2) L triplet with Y = 0 as a benchmark scenario which has rich phenomenological possibilities due to the presence of a light pseudoscalar associated with the Z3 symmetric superpotential. A detailed collider simulation considering all SM backgrounds has been carried out in order to determine which final states are more favourable for observing charged Higgs boson from particular representations as compared with others. We show that different representations can be probed and distinguished via singly-charged Higgs boson phenomenology at the 14 TeV LHC with an earliest data of ∼ 50 fb−1 of integrated luminosity.