Showing papers on "Superpotential published in 2021"

Automorphic forms and fermion masses

Abstract: We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space G/K, where G is a Lie group and K is a compact subgroup of G, modded out by Γ. For a general choice of G, K, Γ and a generic matter content, we explicitly construct a minimal Kahler potential and a general superpotential, for both rigid and local $$ \mathcal{N} $$ = 1 supersymmetric theories. We also specialize our construction to the case G = Sp(2g, ℝ), K = U(g) and Γ = Sp(2g, ℤ), whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing g = 2, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.

Three-dimensional flux vacua from IIB on co-calibrated G2 orientifolds

Abstract: We derive the 3D N = 1 superpotential for the closed string sector of type IIB supergravity on toroidal O5 orientifolds with co-calibrated G2 structure and RR background flux. We find that such compactifications can provide full closed string moduli stabilization on supersymmetric $$\hbox {AdS}_3$$ vacua, and once we include brane-supersymmetry-breaking we also find indication for the existence of classical 3D de Sitter solutions. The latter however are rather difficult to reconcile with the “shape” moduli stabilization and flux quantization. We also discuss the possibility of achieving scale separation in $$\hbox {AdS}_3$$ and $$\hbox {dS}_3$$ vacua, but such effects seem to be hindered by the geometric flux quantization.

Holography for 2D N = ( 0 , 4 ) quantum field theory

Abstract: We study the correspondence between ${\mathrm{AdS}}_{3}$ massive IIA supergravity vacua and two-dimensional $\mathcal{N}=(0,4)$ quiver quantum field theories. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space that provide the dual quiver theory with exactly the correct amount of flavor symmetry in order to cancel its gauge anomalies. Then we propose that the structure of the field theory should be complemented with additional bifundamental matter, which we argue may only be $\mathcal{N}=(4,4)$ hypermultiplets. Finally, we construct a Bogomol'nyi-Prasad-Sommerfield (BPS) string configuration and use the old and new supersymmetric matter to build its dual ultraviolet operator. During this holographic synthesis, we uncover some interesting features of the quiver superpotential and associate the proposed operator with the same classical mass of its dual BPS string.

Large N gauge theories with a dense spectrum and the weak gravity conjecture

Abstract: We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional $$ \mathcal{N} $$ = 1 supersymmetric SU(N) gauge theory with one adjoint and a pair of fundamental/anti-fundamental chiral multiplets. This theory flows to a superconformal theory in the infrared upon a superpotential coupling with gauge singlets. The gap in the low-lying spectrum scales as 1/N and the central charges scale as O(N1) contrary to the usual O(N2) scaling of ordinary gauge theory coming from the matrix degree of freedom. We find the AdS version of the Weak Gravity Conjecture (WGC) holds for this theory, although it cannot be holographically dual to supergravity. This supports the validity of WGC in a more general theory of quantum gravity.

Small flux superpotential in F-theory compactifications

Abstract: We investigate whether a class of models describing F-theory compactifications admits a specific type of flux vacua with an exponentially small vacuum expectation value of the superpotential, by generalizing a method recently developed in type IIB flux compactifications. First we clarify that a restricted choice of ${G}_{4}$-flux components reduces a general flux superpotential into a simple form, which promotes the existence of supersymmetric vacua with one flat direction at the perturbative level. Then we utilize the techniques of mirror symmetry to determine one-instanton corrections to the potential and investigate in detail the vacuum solutions of a particular model.

A 3d disordered superconformal fixed point

Abstract: We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a $$ \mathcal{N} $$ = 2 large N Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large N spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.

Resolving spacetime singularities in flux compactifications & KKLT

Abstract: In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure SU(N) super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of n such exotic branes is given by the (A1, An−1) Argyres-Douglas theory. Moreover, the splitting of the perturbative (in α′) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of $$ \mathcal{O} $$ (1) Einstein frame volume. While this region generically takes up an $$ \mathcal{O} $$ (1) fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential dynamically ensures that the 4d effective field theory of KKLT remains valid nevertheless.

Affleck-Dine inflation in supergravity

Abstract: Affleck-Dine inflation is a recently proposed model in which a single complex scalar field, nonminimally coupled to gravity, drives inflation and simultaneously generates the baryon asymmetry of universe via Affleck-Dine mechanism. In this paper we investigate the supersymmetric implementation of Affleck-Dine inflation in the use of two chiral superfields with appropriate superpotential and K\"ahler potential. The scalar potential has a similar form to the potential of original Affleck-Dine inflation, and it gives successful inflation and baryogenesis. We also consider the isocurvature perturbation evolving after crossing the horizon, and find that it is ignorable and hence consistent with the observations.

Dirac Hamiltonian in a supersymmetric framework

Abstract: We investigate the most general form of the one-dimensional Dirac Hamiltonian HD in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we construct a quasi-Hamiltonian K, defined as the square of HD, to explore the consequences. We show that the diagonal elements of K under a suitable approximation reflect the presence of a superpotential, thus proving a useful guide in unveiling the role of SUSY. For illustrative purposes, we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.

Resolving spacetime singularities in flux compactifications & KKLT

Abstract: In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure $SU(N)$ super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of $n$ such exotic branes is given by the $(A_1,A_{n-1})$ Argyres-Douglas theory. Moreover, the splitting of the perturbative (in $\alpha'$) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of $\mathcal{O}(1)$ Einstein frame volume. While this region generically takes up an $\mathcal{O}(1)$ fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential \textit{dynamically} ensures that the 4d effective field theory of KKLT remains valid nevertheless.

Local G2-manifolds, Higgs bundles and a colored quantum mechanics

Abstract: M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

N $$ \mathcal{N} $$ = 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 − e expansion shows that the U(2) preserving superpotential deformations of the sQED (mod- ulo tuning mass terms to zero) are irrelevant, therefore 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.

Constraining nonrelativistic RG flows with holography

Abstract: We examine nonrelativistic holographic renormalization group (RG) flows by working with Einstein-Maxwell-scalar theories which support geometries that break Lorentz invariance at some energy scale We adopt the superpotential formalism, which helps us characterize the radial flow in this setup and bring to light a number of generic features In particular, we identify several quantities that behave monotonically under RG flow As an example, we show that the index of refraction is generically monotonic We also construct a combination of the superpotentials that flows monotonically in Einstein-scalar theories supporting nonrelativistic solutions and which reduces to the known c-function in the relativistic limit Interestingly, such quantity also exhibits monotonicity in a variety of black hole solutions to the full Einstein-Maxwell-scalar theory, hinting at a deeper structure Finally, we comment on the breakdown of such monotonicity conditions and on the relation to a candidate c-function obtained previously from entanglement entropy

Systematics of type IIB moduli stabilisation with odd axions

Abstract: Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms $(B_2,C_2)$ in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D $\mathcal{N}=1$$F$-term scalar potentials at higher orders in the $\alpha^{\prime}$ and $g_{s}$ expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependences which are induced by fluxes or non-perturbative effects. Initially, we prove the existence of a no-scale structure for odd moduli in the presence of $(\alpha^\prime)^{3}$ corrections to the Kahler potential. By studying a partially $\mathrm{SL}(2,\mathbb{Z})$-completed form of the Kahler potential, we derive the exact no-scale breaking effects at the closed string $1$-loop and non-perturbative D-instanton level. These observations allow us to present rigorous expressions for the $F$-term scalar potential applicable to arbitrary numbers of moduli in type IIB Calabi-Yau orientifold compactifications. Finally, we compute the Hessian for odd moduli and discuss potential phenomenological implications.

Dirac Hamiltonian in a supersymmetric framework

Abstract: We investigate the most general form of the one-dimensional Dirac Hamiltonian $H_D$ in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we construct a quasi-Hamiltonian $\mathcal{K}$, defined as the square of $H_D$, to explore the consequences. We show that the diagonal elements of $\mathcal{K}$ under a suitable approximation reflects the presence of a superpotential thus proving a useful guide in unveiling the role of SUSY. For illustrative purpose we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.

Completing the eclectic flavor scheme of the ℤ2 orbifold

Abstract: We present a detailed analysis of the eclectic flavor structure of the two-dimensional ℤ2 orbifold with its two unconstrained moduli T and U as well as SL(2, ℤ)T × SL(2, ℤ)U modular symmetry. This provides a thorough understanding of mirror symmetry as well as the R-symmetries that appear as a consequence of the automorphy factors of modular transformations. It leads to a complete picture of local flavor unification in the (T, U) modulus landscape. In view of applications towards the flavor structure of particle physics models, we are led to top-down constructions with high predictive power. The first reason is the very limited availability of flavor representations of twisted matter fields as well as their (fixed) modular weights. This is followed by severe restrictions from traditional and (finite) modular flavor symmetries, mirror symmetry, $$ \mathcal{CP} $$ and R-symmetries on the superpotential and Kahler potential of the theory.

Sequential deconfinement in $3d$ $\mathcal{N}\!=\!2$ gauge theories

Abstract: We consider 3d $$ \mathcal{N} $$ = 2 gauge theories with fundamental matter plus a single field in a rank-2 representation. Using iteratively a process of “deconfinement” of the rank-2 field, we produce a sequence of Seiberg-dual quiver theories. We detail this process in two examples with zero superpotential: Usp(2N) gauge theory with an antisymmetric field and U(N) gauge theory with an adjoint field. The fully deconfined dual quiver has N nodes, and can be interpreted as an Aharony dual of theories with rank-2 matter. All chiral ring generators of the original theory are mapped into gauge singlet fields of the fully deconfined quiver dual.

Static spacetimes haunted by a phantom scalar field. III. Asymptotically (A)dS solutions

Abstract: The static and spherically symmetric solutions in the $n(\ensuremath{\ge}4)$-dimensional Einstein-phantom-scalar system fall into three families: (i) the Fisher solution, (ii) the Ellis-Gibbons solution, and (iii) the Ellis-Bronnikov solution. We exploit these solutions as seed to generate a bunch of corresponding asymptotically (A)dS spacetimes, at the price of introducing the potential of the scalar field. Despite that the potentials are different for each solution, each potential is expressed in terms of the superpotential as in supergravity. We discuss the global structure of these solutions in detail and spell out the domain of parameters under which each solution represents a black hole/wormhole. The Ellis-Bronnikov class of solutions presents novel examples of spherical traversable wormholes that interpolate two different (A)dS critical points of the (super)potential.

Pole-Induced Higgs Inflation With Hyperbolic Kaehler Geometries.

Abstract: We present novel realizations of Higgs inflation within Supergravity which are largely tied to the existence of a pole of order two in the kinetic term of the inflaton field. This pole arises due to the selected Kaehler potentials which parameterize the (SU(1,1)/U(1))^2 or SU(2,1)/(SU(2)xU(1)) manifolds with scalar curvatures R_{(11)^2}=-4/N or R_{21}=-3/N respectively. The associated superpotential includes, in addition to the Higgs superfields, a stabilizer superfield, respects the gauge and an R symmetries and contains the first allowed nonrenormalizable term. If the coefficient of this term is almost equal to that of the renormalizable terms within about 10^-5 and N=1, the inflationary observables can be done compatible with the present data and the scale M of gauge-symmetry breaking may assume its value within MSSM. Increasing M beyond this value, though, inflation may be attained with less tuning. Modifications to the Kaehler potentials associated with the manifolds above allow for inflation, realized with just renormalizable terms, resulting to higher tensor-to-scalar ratios as N approaches its maximum at N=40.

Revisit on two-dimensional self-gravitating kinks: superpotential formalism and linear stability

Abstract: Self-gravitating kink solutions of a two-dimensional dilaton gravity are revisited in this work. Analytical kink solutions are derived from a concise superpotential formalism of the dynamical equations. A general analysis on the linear stability is conducted for an arbitrary static solution of the model. After gauge fixing, a Schrodinger-like equation with factorizable Hamiltonian operator is obtained, which ensures the linear stability of the solution.

Noether's Theorems and Energy in General Relativity

Abstract: This paper has three main aims: first, to give a pedagogical introduction to Noether's two theorems and their implications for energy conservation in general relativity, which was a central point of discussion between Hilbert, Klein, Noether and Einstein. Second, it introduces and compares two proposals for gravitational energy and momentum, one of which is very influential in physics: and, so far as I know, neither of the two has been discussed in the philosophical literature. Third, it assesses these proposals in connection with recent philosophical discussions of energy and momentum in general relativity. After briefly reviewing the debates about energy conservation between Hilbert, Klein, Noether and Einstein, I give Noether's two theorems. I show that Einstein's gravitational energy-momentum pseudo-tensor, including its superpotential, is fixed, through Noether's theorem, by the boundary terms in the action. That is, the freedom to add an arbitrary superpotential to the gravitational pseudo-tensor corresponds to the freedom to add boundary terms to the action without changing the equations of motion. This freedom is fixed in the same way for both problems. I also review two proposals for energy and momentum in GR, of which one is a quasi-local alternative to the local expressions, and the other builds on Einstein's local pseudo-tensor approach. I discuss the recent philosophical literature on the conservation of energy and momentum in general relativity, and I assess and compare the two proposals in the light of this literature: especially, in light of questions about diffeomorphism invariance and background-independence.

London Moment, London’s Superpotential, Nambu-Goldstone Mode, and Berry Connection from Many-Body Wave Functions

Abstract: Although the standard theory of superconductivity based on the BCS theory is a successful one, there are several experimental results that indicate the necessity for fundamental revisions. One of them is the mass in the London moment. Experiments indicate the mass in the London moment is the free electron mass although the BCS theory and its extension predict it to be an effective mass. We show that this discrepancy is lifted if we install the London’s superpotential in the theory, and identify it as the Berry phase arising from the many-body wave functions. Then, the induced current by the applied magnetic field becomes a stable current calculated using the free energy in contrast to the linear response current assumed in the standard theory which yields the Nambu-Goldstone mode. The Nambu-Goldstone mode arising from the breakdown of the global U(1) gauge invariance in the standard theory is replaced by the collective mode arising from the Berry connection. Then, the free electron mass appears in the London moment.

Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

Abstract: We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a ℤ2-symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $$ \overline{g} $$ , and is expected to have a critical point at a tuned value $$ {\overline{g}}_{\ast } $$ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the ℤ2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $$ \overline{g} $$ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C-function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

Exact holographic RG flows in extended SUGRA

Abstract: We present a family of exact planar hairy neutral black hole solutions in extended supergravity with Fayet-Iliopoulos (FI) terms. We consider a model where the magnetic part of FI sector vanishes and obtain the superpotential at finite temperature in analytic form. Then, we discuss the thermodynamics and some holographic properties of these solutions. We regularize the action by two different methods, one with gravitational and scalar counterterms and the other using the thermal superpotential as a counterterm, and compute the holographic stress tensor. We also construct the c-function of the corresponding RG flow and obtain an exact holographic β-function for this model.

Enumerative geometry of del Pezzo surfaces

Abstract: We prove an equivalence between the superpotential defined via tropical geometry and Lagrangian Floer theory for special Lagrangian torus fibres in del Pezzo surfaces constructed by Collins-Jacob-Lin. We also include some explicit calculations for the projective plane, which confirm some folklore conjecture in this case.

Cosmology of the string derived flipped SU(5)

Abstract: We study the cosmology of a string derived supersymmetric flipped $SU(5)$ model in the context of free-fermionic heterotic constructions that allow full calculability of the effective supergravity in perturbation theory around the fermionic vacuum where all string moduli have fixed values. The model has 3 generations of chiral families and a Higgs sector leading to particle phenomenology consistent with low energy data, that has been extensively studied in the past. Here, we show that it can also accommodate a novel successful cosmology, based on the no-scale effective supergravity derived from string theory as well as an appropriate induced superpotential suppressed by five powers of the string scale. It utilises two gauge singlet chiral superfields present in the low energy spectrum: the inflaton $y$, identified as the superpartner of a state mixed with R-handed neutrinos, %of the heaviest generation, and the goldstino $z$ with a superpotential of the form $W_I=M_I z(y-\lambda y^2)$ (in supergravity units) where $\lambda$ is a dimensionless ${\cal O}\left(1\right)$ parameter and $M_I$ the mass scale of inflation generated at 5th order by the breaking of an anomalous $U(1)_A$ gauge symmetry, characteristic of heterotic string chiral vacua. The resulting scalar potential leads to Starobinsky type inflation. Our results can be easily generalised to a large class of models with similar properties.

Small Cosmological Constants in String Theory

Abstract: We construct supersymmetric $\mathrm{AdS}_4$ vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the $\alpha'$ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude $ < 10^{-123}$ in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

Full phase diagram of a UV completed N $$ \mathcal{N} $$ = 1 Yang-Mills-Chern-Simons matter theory

Abstract: We study the large N phase diagram of an asymptotically free UV completion of $$ \mathcal{N} $$ = 1 SU(N) super-Yang-Mills-Chern-Simons theory coupled to a single massive fundamental scalar multiplet with a quartic superpotential coupling. We compute the effective superpotential at small gauge coupling λ ≡ N/k, and combine this with previous results in the literature to obtain the full phase diagram in this regime. We find that tuning the UV parameters allows us to reach various phases and fixed points of Chern-Simons theory that were recently discovered using large N techniques, as well as new phases that characterize the Yang-Mills theory. We also conjecture the form of the phase diagram for general values of λ and for finite N.