We study N=1 supersymmetric U(N) gauge theories coupled to an adjoint chiral field with superpotential. We consider the full supersymmetric moduli space of these theories obtained by adding all allowed chiral operators. These include higher-dimensional operators that introduce a field-dependence for the gauge coupling. We show how Feynman diagram/matrix model/string theoretic techniques can all be used to compute the IR glueball superpotential. Moreover, in the limit of turning off the superpotential, this leads to a deformation of N=2 Seiberg-Witten theory. In the case where the superpotential drives the squared gauge coupling to a negative value, we find that supersymmetry is spontaneously broken, which can be viewed as a novel mechanism for breaking supersymmetry. We propose a new duality between a class of N=1 supersymmetric U(N) gauge theories with field-dependent gauge couplings and a class of U(N) gauge theories where supersymmetry is softly broken by nonzero expectation values for auxiliary components of spurion superfields.
We study the SUSY/non-SUSY duality proposed by Aganagic et al. from Type IIA string and M-theory perspectives. We find that our brane configuration generalizes the so-called $extended$ Seiberg-Witten theory on the one hand, and provides a way to realize non-SUSY vacua by intersecting NS5-branes on the other hand. We also argue how the partial SUSY breaking from $\Ncal=2$ down to $\Ncal=1$ can be clearly visualized through the brane picture.
A generic lesson of string theory is that the coupling constants of an effective low energy theory are determined by the vacuum values of a set of fields - the so-called moduli - some of which are stabilized at relatively low masses by non-perturbative effects. We argue that the physics of these moduli cannot be separated from the issues of dynamical and gauge mediated supersymmetry breaking. To illustrate this point we present a modified version of the type IIB KKLT model where the criteria for gauge mediated SUSY breaking may be realized.
We study the vacuum structure of the U(N) gauge model with partially broken N=2 supersymmetry. From the analysis of the classical vacua of this model, we point out that in addition to the ordinary N=1 supersymmetric vacua, there are vacua with negative gauge coupling constants, which preserve another N=1 supersymmetry. These latter vacua can be analyzed by using SUSY/non-SUSY duality which is recently proposed by Aganagic, Beem, Seo and Vafa. A dual description of these in UV is U(N) gauge theory where the supersymmetry is broken by spurion superfields. Following them, we see that there are su…
We present a dual description for $SU(N)$ supersymmetric gauge theory with an antisymmetric tensor and fundamentals, and no superpotential. This duality is derived from the dualities of Seiberg. Under a perturbation of the superpotential, the dual theory breaks supersymmetry at tree level.
We suggest an alternative approach to deconfine N =1 SU(N) supersymmetric gauge theory with a symmetric tensor, fundamentals, anti-fundamentals, and no superpotential. It is found that although the dual prescription derived by this new method of deconfinement is different from that by the original method, both dual prescriptions are connected by duality transformations. By deforming the theory, it is shown that both dual theories flow properly so that the Seiberg's duality is preserved.
We give a simple proof of the relation $Λ\p_artialΛ\F= {i\over2π}b_1\langle\Trϕ^2\rangle$, which is valid for $N=2$ supersymmetric QCD with massless quarks. We consider $SU(N_c)$ gauge theories as well as $SO(N_c)$ and $SP(N_c)$. Aa analogous relation which corresponds to massive hypermultiplets is written down. We also discuss the generalizations to $N=1$ models in the Coulomb phase.
We study the influence of anomalous U(1) symmetries and their associated D-terms on the vacuum structure of global field theories once they are coupled to N=1 supergravity and in the context of string compactifications with moduli stabilisation. In particular, we focus on a IIB string motivated construction of the ISS scenario and examine the influence of one additional U(1) symmetry on the vacuum structure. We point out that in the simplest one-Kahler modulus compactification, the original ISS vacuum gets generically destabilised by a runaway behaviour of the potential in the modulus directio…
We study the asymptotic limits of the heterotic string theories compactified on tori. We find a bilinear form uniquely determined by dualities which becomes Lorentzian in the case of one spacetime dimension. For the case of the SO(32) theory, the limiting descriptions include SO(32) heterotic strings, type I, type IA and other T-duals, M-theory on K3, type IIA theory on K3 and type IIB theory on K3 and possibly new limits not understood yet.
This brief review deals with prepotentials inspired by N=1 SUSY considerations due to Cachazo, Intrilligator, Vafa. These prepotentials associated with matrix models following Dijkgraaf and Vafa should be considered as given on an enlarged moduli space that includes Whitham times (couplings of the superpotential). This moduli space is nothing but the whole moduli space of (decorated) hyperelliptic curves. Corresponding prepotentials are logarithms of (quasiclassical) tau-functions and satisfy the WDVV equations.
After an introduction to N=2 susy Yang-Mills theories, I review in some detail, for the SU(2) gauge group, how the low-energy effective action is obtained using duality and the constraints arising from the supersymmetry. Then I discuss how knowledge of this action, duality and certain discrete symmetries allow us to determine the spectra of stable BPS states at any point in moduli space. This is done for gauge group SU(2), without and with fundamental matter hypermultiplets which may have non-vanishing bare masses. In the latter case non-trivial four-dimensional CFTs arise at Argyres-Douglas t…
We elaborate on the recently discovered spinor-vector duality in realistic free fermionic heterotic vacua. We emphasize the interpretation of the freely-acting orbifolds carried out on the six internal dimensions as coordinate-dependent compactifications; they play a central role in the duality, especially because of their ability to break the right-moving superconformal algebra of the space-time supersymmetric heterotic vacua. These considerations lead to a simple and intuitive proof of the spinor-vector duality, and to the formulation of explicit rules to find the dual of a given model. We d…
We consider the action of a non-abelian T-duality on backgrounds with an AdS${}_5$ factor in type IIA supergravity, finding a new type IIB background, as well as the non-abelian T-dual of a domain wall solution which has as limits the non-abelian T-dual of $AdS_5\times T^{1,1}$ and the non-abelian T-dual of $AdS_3\times \mathbb{R}^2\times S^2\times S^3$. We explore some consequences of non-abelian T-duality for the dual conformal field theories.
We study supersymmetric AdS$_7$ vacua of massive type IIA string theory, which were argued to describe the near-horizon limit of NS5/D6/D8-brane intersections and to be holographically dual to 6D $(1,0)$ theories. We show, for the case without D8-brane charges, that such vacua do not admit any supersymmetry-breaking deformations. Our result implies that the dual $(1,0)$ theories do not have a conformal manifold, thus extending previously known results for supersymmetric deformations. It is also in line with the recent conjecture that non-supersymmetric AdS vacua are in the swampland.
We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for all beta, assuming the existence of an interacting Spin(8) invariant fixed point at the origin. The resulting formulae are manifestly invariant under the SL(2,Z) duality of four dimensional N=4 SYM and lead to interesting quantitative predictions for instanton effects in gauge theory and in Type II string theory.
We analyze in detail the moduli space of vacua of N=2 SUSY QCD with n_c colors and n_f flavors. The Coulomb branch has submanifolds with non-Abelian gauge symmetry. The massless quarks and gluons at these vacua are smoothly connected to the underlying elementary quarks and gluons. Upon breaking N=2 by an N=1 preserving mass term for the adjoint field the theory flows to N=1 SUSY QCD. Some of the massless quarks and gluons on the moduli space of the N=2 theory become the magnetic quarks and gluons of the N=1 theory. In this way we derive the duality in N=1 SUSY QCD by identifying its crucial bu…
We discuss duality in $N=1$ SUSY gauge theories in Seiberg's conformal window, $(3N_c/2)<N_f<3N_c$. The 't Hooft consistency conditions -- the basic tool for establishing the infrared duality -- are considered taking into account higher order $α$ corrections. The conserved (anomaly free) $R$ current is built to all orders in $α$. Although this current contains all orders in $α$ the 't Hooft consistency conditions for this current are shown to be one-loop. This observation thus justifies Seiberg's matching procedure. We also briefly discuss the inequivalence of the ``electric" and ``magnetic" t…
We study moduli-dominated SUSY breaking within the framework of string models. This type of SUSY breaking in general leads to non-universal soft masses, i.e. soft scalar masses and gaugino masses. Further gauginos are lighter than sfermions. This non-universality has phenomenologically important implications. We investigate radiative electroweak symmetry breaking in the mass spectrum derived from moduli-dominated SUSY breaking, where the lightest chargino and neutralino are almost gauginos. Moreover, constraints from the branching ratio of $b \to s γ$ and the relic abundance of the LSP are als…
We study Yukawa unification in string models with moduli-dominant SUSY breaking. This type of SUSY breaking in general leads to non-universal soft masses, i.e., soft scalar masses and gaugino masses. Such non-universality is important for phenomenological aspects of Yukawa unification, i.e., successful electroweak breaking, SUSY corrections to the bottom mass and the branching ratio of $b \to s γ$. We show three regions in the whole parameter space which lead to successful electroweak breaking and allow small SUSY corrections to the bottom mass. For these three regions we investigate the $b \t…
There is a close relation between duality in $N=2$ SUSY gauge theories and integrable models. In particular, the quantum moduli space of vacua of $N=2$ SUSY $SU(3)$ gauge theories coupled to two flavors of massless quarks in the fundamental representation can be related to the spectral curve of the Goryachev-Chaplygin top. Generalizing this to the cases with {\it massive} quarks, and $N_f = 0,1,2$, we find a corresponding integrable system in seven dimensional phase space where a hyperelliptic curve appears in the Painlevé test. To understand the stringy origin of the integrability of these th…
These are notes from introductory lectures given at the Ecole Normale in Paris and at the Strasbourg meeting dedicated to the memory of Claude Itzykson. I review in considerable detail and in a hopefully pedagogical way the work of Seiberg and Witten on $N=2$ supersymmetric $SU(2)$ gauge theory without extra matter. This presentation basically follows their original work, except in the last section where the low-energy effective action is obtained emphasizing more the relation between monodromies and differential equations rather than using elliptic curves.
We present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton effects are related to the bulk contribution to the index which counts BPS dyons in the corresponding four dimensional theory. In both cases, the calculations provide semiclassical tests of recently proposed exact results for the lowest non-trivial terms in the derivative expansion of the Wilsonian effective action.
In this talk I review and generalize an idea of Seiberg that an N=1 supersymmetric gauge theory shows confinement without breaking of chiral symmetry when the gauge symmetry of its magnetic dual is completely broken by the Higgs effect. It is shown how the confining spectrum of a supersymmetric gauge theory can easily be derived when a magnetic dual is known and this method is applied to many models containing fields in second rank tensor representations and an appropriate tree-level superpotential.
Using the low energy effective action of the N=2 supersymmetric SU(2) Yang-Mills theory we calculate the free energy at finite temperature, both in the semiclassical region and in the dual monopole/dyon theory. In all regions the free energy depends on both the temperature T and the appropriate moduli parameter, and is thus minimized only for specific values of the moduli parameter, in contrast to the T=0 case where the energy vanishes all over the moduli space. Within the validity of perturbation theory, we find that the finite temperature Yang-Mills theory is stable only at definite points i…
We study the patterns in the duality of a wide class of N=1 supersymmetric gauge theories in four dimensions. We present many new generalizations of the classic duality models of Kutasov and Schwimmer, which have themselves been generalized numerous times in works of Intriligator, Leigh and the present authors. All of these models contain one or two fields in a two-index tensor representation, along with fields in the defining representation. The superpotential for the two-index tensor(s) resembles A_k or D_k singularity forms, generalized from numbers to matrices. Looking at the ensemble of t…
We expand on an idea of Seiberg that an N=1 supersymmetric gauge theory shows confinement without breaking of chiral symmetry when the gauge symmetry of its magnetic dual is completely broken by the Higgs effect. This has recently been applied to some models involving tensor fields and an appropriate tree-level superpotential. We show how the confining spectrum of a supersymmetric gauge theory can easily be derived when a magnetic dual is known and we determine it explicitly for many models containing fields in second rank tensor representations. We also give the form of the confining superpot…
We study the moduli space of three-dimensional $\mathcal{N}=2$ SQCD with $SU(N)$ gauge group and $F<N$ massless flavors. In the case of an $SU(2)$ theory with a single massless flavor, we explicitly calculate the quantum constraint $YM=1$ and generalize the calculation to models with arbitrary $N$ and $F=N-1$ flavors. In theories with $F<N-1$ flavors, we find that analogous constraints exist in locally defined coordinate charts of the moduli space. The existence of such constraints allows us to show that the Coulomb branch superpotential generated by single monopole effects is equivalent to th…
We study an exactly marginal deformation of N=4 SUSY Yang-Mills with gauge group U(N) using field theory and string theory methods. The classical theory has a Higgs branch for rational values of the deformation parameter. We argue that the quantum theory also has an S-dual confining branch which cannot be seen classically. The low-energy effective theory on these branches is a six-dimensional non-commutative gauge theory with sixteen supercharges. Confinement of magnetic and electric charges, on the Higgs and confining branches respectively, occurs due to the formation of BPS-saturated strings…
Low--energy limits of N=2 supersymmetric field theories in the Higgs branch are described in terms of a non--linear 4--dimensional sigma--model on a \hk target space, classically obtained as a \hk quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low--energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg--Witten $SU(2)$ theory with $N_f$ flavors, interpreted by Witten as a small instan…
We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold singularities. At these singular points in moduli space the theory exhibits a duality cascade and flows to a confining theory with a mass gap. By exactly solving the corresponding holomorphic matrix model we compute the exact quantum superpotential generated at the end of the duality cascade an…
We propose a new chiral model of metastable supersymmetry breaking in the conformal window via chiral/nonchiral Seiberg duality, which is focused on Spin(7)/SU(N_f-4) duality in this letter. Following the approach of Intriligator-Seiberg-Shih model, a small mass perturbation in the nonchiral theory leads to supersymmetry breaking by rank condition in the chiral dual description.
We discuss the physics of moduli (light scalar fields with Planck-suppressed couplings to matter) in the case of low-scale supersymmetry breaking such as gauge mediation. We argue that even if the mechanism of moduli stabilization is decoupled from the mechanism of SUSY breaking, moduli masses will generically be parametrically related to the gravitino mass once the cancellation of the cosmological constant is taken into account. For low- scale SUSY breaking, this implies that moduli fields are light, long-lived relics that will generically drive the universe into a matter-dominated phase, in …
Many N=1 heterotic string compactifications exhibit physically mysterious singularities at codimension one in the moduli space of vacua. At these singularities, Yukawa couplings of charged fields develop poles as a function of the moduli. We explain these conformal field theory singularities, in a class of examples, as arising from non-perturbative gauge dynamics of non-perturbative gauge bosons (whose gauge coupling is the sigma model coupling) in the string theory.
T-duality (Fourier-Mukai duality) and properties of classical instanton moduli spaces can be used to deduce some properties of $α^{\prime}$-corrected moduli spaces of branes for Type IIA string theory compactified on $K3$ or $T^4$. Some interesting differences between the two compactifications are exhibited.
The low energy structures of N=1 supersymmetric models with E_6, F_4 and E_7 gauge groups and fundamental irrep matter contents are studied herein. We identify sets of gauge invariant composites which label all flat directions in the confining/Higgs phases of these theories. The impossibility of mapping several of these primary operators rules out previously conjectured exceptional self duals reported in the literature.
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partitio…
Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed points on moduli space with non-vanishing flux. We also discuss the more general target space dualities associated with these fixed points.
The ${\cal N}=1$ SUSY nonlinear sigma models in four spacetime dimensions are studied to obtain BPS walls and junctions. A nonlinear sigma model with a single chiral scalar superfield is found which has a moduli space of the topology of $S^1$ and admits BPS walls and junctions connecting arbitrary points in moduli space. New BPS junction solutions connecting $N$ discrete vacua are also found for nonlinear sigma models with several chiral scalar superfields. More detailed exposition of our results can be found in Ref.\cite{NNS}.
In certain class of flux compactification, moduli mediated supersymmetry (SUSY) breaking preserves flavor and CP at leading order in the perturbative expansion controlled by the vacuum expectation value of the messenger modulus. Nevertheless there still might be dangerous flavor or CP violation induced by higher order Kähler potential. We examine the constraints on such SUSY breaking scheme imposed by low energy flavor and/or CP violating observables. It is found that all phenomenological constraints can be satisfied even for generic form of higher order Kähler potential and sparticle spectra …
We consider \caln=1 supersymmetric SO(N) gauge theory with a symmetric traceless tensor. This theory saturates 't Hooft matching conditions at the origin of the moduli space. This naively suggests a confining phase, but Brodie, Cho, and Intriligator have conjectured that the origin of the moduli space is in a Non-Abelian Coulomb phase. We construct a dual description by the deconfinement method, and also show that the theory indeed has an infrared fixed point for certain values of N. This result supports their argument.
We show how the supersymmetric KdV equation can be obtained from the self-duality condition on Yang-Mills fields in four dimension associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of Susy KdV equations from such a condition. We formulate the Susy KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self-duality condition in four dimension can also lead to these equations.
We discuss the coupling of heavy moduli fields to light fields when the dynamics of the latter, absent such couplings, yields metastable vacua. We show that the survival of the vacuum structure of the local model depends nontrivially on the cross-couplings of the two sectors. In particular we find that for "local" models (such as those realized by D-branes in type II string theories) with metastable vacua breaking supersymmetry via F-terms, cross-coupling of the two sectors at an intermediate scale can push the metastable vacuum outside of the regime of the effective field theory. We parametri…
We here generalize our previous construction [hep-th/0409019] of non-supersymmetric $p$-branes delocalized in one transverse spatial direction to two transverse spatial directions in supergravities in arbitrary dimensions ($d$). These solutions are characterized by five parameters. We show how these solutions in $d=10$ interpolate between D($p+2$)-anti-D($p+2$) brane system, non-BPS D$(p+1)$-branes (delocalized in one direction) and BPS D$p$-branes by adjusting and scaling the parameters in suitable ways. This picture is very similar to the descent relations obtained by Sen in the open string …
We investigate neutralino dark matter from a string/M-theory perspective. Using the Kallosh-Linde (KL) scenario to stabilize the string moduli requires supersymmetry breaking for uplifting to a de Sitter vacuum. We consider the free magnetic dual description of $\mathcal{N}=1$ SUSY QCD with massive flavours, the Intriligator-Seiberg-Shih model (ISS), as an F-term dynamical SUSY breaking sector. This framework allows for a gravitino mass in the TeV range. Moreover, due to the plethora of particles from the ISS sector, we investigate the consequences of coupling the MSSM with the KL-ISS setup to…
We present a direct computation of the period integrals on degenerate Seiberg-Witten curves for supersymmetric QCD, and show how these periods determine the changes in the quantum numbers of the states, when passing from the weak to the strong-coupling domains in the mass moduli space of the theory. The confinement of monopoles at strong coupling is discussed, and we demonstrate that the ambiguities in choosing the way in the moduli space do not influence to the physical conclusions on confinement of monopoles in the phase with the condensed light dyons.
We study how dynamically breaking SQCD can be obtained on two intersecting seven-branes in F-theory. In the mechanism which we present in this paper one of the seven-branes is responsible for producing the low-energy gauge group and the other one is for generating vector bundle moduli. The fundamental matter charged under the gauge group is localized on the intersection. The mass of the matter fields is controlled by the vector bundle moduli. The analysis of under what conditions a sufficient number of the fundamental flavors becomes light turns out to be equivalent to the analysis of non-pert…
The moduli of N=1 compactifications of IIB string theory can be stabilized by a combination of fluxes (which freeze complex structure moduli and the dilaton) and nonperturbative superpotentials (which freeze Kahler moduli), typically leading to supersymmetric AdS vacua. We show that stringy corrections to the Kahler potential qualitatively alter the structure of the effective scalar potential even at large volume, and can give rise to non-supersymmetric vacua including metastable de Sitter spacetimes. Our results suggest an approach to solving the cosmological constant problem, so that the sca…
We consider a non-supersymmetric USp Yang-Mills Chern-Simons gauge theory coupled to fundamental flavours. The theory is realised in type IIB string theory via an embedding in a Hanany-Witten brane configuration which includes an orientifold and anti-branes. We argue that the theory admits a magnetic Seiberg dual. Using the magnetic dual we identify dynamics in field theory and brane physics that correspond to various phases, obtaining a better understanding of 3d bosonization and dynamical breaking of flavour symmetry in USp QCD$_3$ theory. In field theory both phases correspond to magnetic '…
We study the most general renormalizable ${\cal N}=1$ $U(N)$ Chern-Simons gauge theory coupled to a single (generically massive) fundamental matter multiplet. At leading order in the 't Hooft large $N$ limit we present computations and conjectures for the $2 \times 2$ $S$ matrix in these theories; our results apply at all orders in the 't Hooft coupling and the matter self interaction. Our $S$ matrices are in perfect agreement with the recently conjectured strong weak coupling self duality of this class of theories. The consistency of our results with unitarity requires a modification of the u…
The values of the $T$ and $U$ moduli are studied for those ${\bf Z}_N $ Coxeter orbifolds with the property that some of the twisted sectors have fixed planes for which the six-torus ${\bf T}^6 $ can not be decomposed into a direct sum ${\bf T}^2\bigoplus {\bf T}^4 $ with the fixed plane lying in ${\bf T}^2 $. Such moduli in general transform under a subgroup of the modular group $SL(2,Z).$ The moduli are determined by minimizing the effective potential derived from a duality invariant gaugino condensate.
We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang-Mills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the D-brane bubbles. Different regions of moduli space are associated with D5-branes of various topologies; singularities in the moduli space are associated with topology change. T-duality on toroidal topologies maps between mirror string realizations of the field theory.
We study a new mechanism to dynamically break supersymmetry in the E8xE8 heterotic string. As discussed recently in the literature, a long-lived, meta-stable non-supersymmetric vacuum can be achieved in an N=1 SQCD whose spectrum contains a sufficient number of light fundamental flavors. In this paper, we present, within the context of the hidden sector of the weakly and strongly coupled heterotic string, a slope-stable, holomorphic vector bundle on a Calabi-Yau threefold for which all matter fields are in the fundamental representation and are massive at generic points in moduli space. It is …
The region of moduli space of string theories which is most likely to describe the "real world" is where the string coupling is about unity and the volume of extra compact dimensions is about the same size as the string volume. Here we map the landscape of this "central" region in a model-independent way, assuming only that the string coupling and compact volume moduli are chiral superfields of N=1 supergravity in 4 dimensions, and requiring only widely accepted conditions: that the supersymmetry (SUSY) breaking scale is about the weak scale and that the cosmological constant be of acceptably …
Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on the dual modules associated with the dual noncommutative flows. Moreover the result is also affirmative in the case of multiflows. As an important application, computed are the moduli spaces of the instanton bundles over the noncommutative Euclidean 4-space with respect to the canonical action of space translations without using the ADHM-construction.
We construct local operators in short representations of supersymmetry algebras from polyvector fields on the quantum moduli space of vacua of supersymmetric gauge theories. These operators form a super Lie algebra under a natural bracket operation with structure constants determined by terms in the operator product expansion of the corresponding operators. We propose a formula for the superconformal index in terms of an index over polyvector fields on the moduli space of vacua. Along the way, we construct several models with moduli space of vacua corresponding to affine cones over smooth base…
I discuss several issues concerning the use of string models as unified theories of all interactions. After a short review of gauge coupling unification in the string context, I discuss possible motivations for the construction of $SU(5)$ and $SO(10)$ String-GUTs. I describe the construction of such String-GUTs using different orbifold techniques and emphasize those properties which could be general. Although $SO(10)$ and $SU(5)$ String-GUTs are relatively easy to build, the spectrum bellow the GUT scale is in general bigger than that of the MSSM and includes colour octets and $SU(2)$ triplets…
We perform a comprehensive and systematic analysis of the SUSY flavor structure of generic 5D supergravity models on $S^1/Z_2$ with multiple $Z_2$-odd vector multiplets that generate multiple moduli. The SUSY flavor problem can be avoided due to contact terms in the 4D effective Kähler potential peculiar to the multi-moduli case. A detailed phenomenological analysis is provided based on an illustrative model.
We present an efficient method for computing the duality group $Γ$ of the moduli space \cM for strings compactified on a Calabi-Yau manifold described by a two-moduli deformation of the quintic polynomial immersed in $\CP(4)$, $\cW={1\over5}(\iy_1^5+\cdots+\iy_5^5)-a\,\iy_4^3 \iy_5^2 -b\, \iy_4^2 \iy_5^3$. We show that $Γ$ is given by a $3$--dimensional representation of a central extension of $B_5$, the braid group on five strands.
We generalize the ISS model of spontaneous supersymmetry breaking to lower dimensions. We also comment on the dynamics of the corresponding brane systems in string theory, and on possible applications to gauge/gravity duality.
Heterotic string compactifications on a $K3$ surface $\mathfrak{S}$ depend on a choice of hyperkähler metric, anti-self-dual gauge connection and Kalb-Ramond flux, parametrized by hypermultiplet scalars. The metric on hypermultiplet moduli space is in principle computable within the $(0,2)$ superconformal field theory on the heterotic string worldsheet, although little is known about it in practice. Using duality with type II strings compactified on a Calabi-Yau threefold, we predict the form of the quaternion-Kähler metric on hypermultiplet moduli space when $\mathfrak{S}$ is elliptically fib…
A naive dimensional reduction of the $N=1, D=10$ supergravity theory that naturally arises in five-brane models is used to determine the rôle of two fields which are basic ingredients of string models: the dilaton and, among the moduli, the breathing mode. It is shown that, under the duality transformation that relates five-branes and strings, these two fields exchange the rôles of 10-dimensional dilaton and radius of the compact manifold. A description of this phenomenon in terms of the linear multiplets of the 4-dimensional supergravity is also presented.
