arXiv subjects
Publications and source records attributed to Matteo Sacchi.
We introduce an algorithm to piecewise dualise linear quivers into their mirror dual. The algorithm uses two basic duality moves and the properties of the $S$-wall which can all be derived by iterative applications of Seiberg-like dualities.
The Higgs branch of 4d $\mathcal{N}=2$ SCFTs can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class $\mathcal{S}$ theory with four or more $\mathbb{Z}_2$-twisted punctures, they do not match. We construct 3d mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4d theory. We further construct $a=c$ theories in class $\mathcal{S}$ using the twisted punctures, and these theories, which includes the $\hat{D}_4(SU(2n+1))$ theories, have Hall--Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all $a=c$ theories with non-empty Higgs branch, including $\mathcal{N}\ge 3$ SCFTs.
In this paper we present various $4d$ $\mathcal{N}=1$ dualities involving theories obtained by gluing two $E[USp(2N)]$ blocks via the gauging of a common $USp(2N)$ symmetry with the addition of $2L$ fundamental matter chiral fields. For $L=0$ in particular the theory has a quantum deformed moduli space with chiral symmetry breaking and its index takes the form of a delta-function. We interpret it as the Identity wall which identifies the two surviving $USp(2N)$ of each $E[USp(2N)]$ block. All the dualities are derived from iterative applications of the Intriligator--Pouliot duality. This plays for us the role of the fundamental duality, from which we derive all others. We then focus on the $3d$ version of our $4d$ dualities, which now involve the $\mathcal{N}=4$ $T[SU(N)]$ quiver theory that is known to correspond to the $3d$ $S$-wall. We show how these $3d$ dualities correspond to the relations $S^2=-1$, $S^{-1}S=1$ and $T^{-1} S T=S^{-1} T S$ for the $S$ and $T$ generators of $SL(2,\mathbb{Z})$. These observations lead us to conjecture that $E[USp(2N)]$ can also be interpreted as a $4d$ $S$-wall.
The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis (ABJ) and related theories, with at least $\mathcal{N}=6$ supersymmetry in three dimensions, are examined in detail. Starting from well-known dualities between theories with orthogonal and symplectic gauge groups and those with unitary gauge groups, we gauge their one-form symmetries or their subgroups and obtain new dualities. One side of the latter involves theories with special orthogonal and symplectic gauge groups, and the other side involves theories with unitary gauge groups; there is a discrete quotient on one or both sides of the duality. We study the refined superconformal indices of such theories and map the symmetries across the dualities, with particular attention to their discrete part. As a generalisation, we also find a new duality between a circular quiver with a discrete quotient of alternating special orthogonal and symplectic gauge groups and a three-dimensional $\mathcal{N}=4$ circular (Kronheimer-Nakajima) quiver with unitary gauge groups, whose Higgs or Coulomb branch describes an instanton on a singular orbifold.
We study the $3d$ $\mathcal{N}=2$ theories resulting from the compactification of a family of $5d$ SCFTs on a torus with flux in the global symmetry. The family of $5d$ SCFTs used in the analysis is the one that UV completes the $5d$ $SU(N+1)$ gauge theories with Chern--Simons level $k$ and $N_f$ fundamental hypermultiplets, generalizing the previous investigation of the torus compactifications of the rank 1 Seiberg $E_{N_f+1}$ SCFT (which is the $N=1$ member of the family). This construction systematically yields three-dimensional theories presenting highly non-trivial non-perturbative phenomena such as infra-red dualities and enhanced symmetries, which we check using various methods.
We consider compactifications of rank $Q$ E-string theory on a genus zero surface with no punctures but with flux for various subgroups of the $\text{E}_8\times \text{SU}(2)$ global symmetry group of the six dimensional theory. We first construct a simple Wess-Zumino model in four dimensions corresponding to the compactification on a sphere with one puncture and a particular value of flux, the cap model. Using this theory and theories corresponding to two punctured spheres with flux, one can obtain a large number of models corresponding to spheres with a variety of fluxes. These models exhibit interesting IR enhancements of global symmetry as well as duality properties. As an example we will show that constructing sphere models associated to specific fluxes related by an action of the Weyl group of $\text{E}_8$ leads to the S-confinement duality of the $\text{USp}(2Q)$ gauge theory with six fundamentals and a traceless antisymmetric field. Finally, we show that the theories we discuss possess an $\text{SU}(2)_{\text{ISO}}$ symmetry in four dimensions that can be naturally identified with the isometry of the two-sphere. We give evidence in favor of this identification by computing the `t Hooft anomalies of the $\text{SU}(2)_{\text{ISO}}$ in 4d and comparing them with the predicted anomalies from 6d.
We present various 4d $\mathcal{N}=1$ theories enjoying IR global symmetry enhancement. The models we consider have the $USp(2n)$ gauge group, 8 fundamental, one antisymmetric chirals and various numbers of gauge singlets. By suitably turning on superpotential deformations involving the singlets which break part of the UV symmetry we flow to SCFTs with $E_6$, $SO(10)$, $SO(9)$, $SO(8)$ and $F_4$ IR global symmetry. We explain these patterns of symmetry enhancement following two arguments due to Razamat, Sela and Zafrir. The first one involves the study of the relations satisfied by marginal operators, while the second one relies on the existence of self-duality frames.
Building on recent progress in the study of compactifications of $6d$ $(1,0)$ superconformal field theories (SCFTs) on Riemann surfaces to $4d$ $\mathcal{N}=1$ theories, we initiate a systematic study of compactifications of $5d$ $\mathcal{N}=1$ SCFTs on Riemann surfaces to $3d$ $\mathcal{N}=2$ theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $E_{N_f+1}$ SCFTs on tori and tubes with flux in their global symmetry, and put the resulting $3d$ theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the $3d$ theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding $5d$ SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the $5d$ picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other $5d$ SCFT that has a deformation leading to a $5d$ gauge theory.
Argyres-Douglas (AD) theories constitute an infinite class of superconformal field theories in four dimensions with a number of interesting properties. We study several new aspects of AD theories engineered in $A$-type class $\mathcal{S}$ with one irregular puncture of Type I or Type II and also a regular puncture. These include conformal manifolds, structures of the Higgs branch, as well as the three dimensional gauge theories coming from the reduction on a circle. The latter admit a description in terms of a linear quiver with unitary and special unitary gauge groups, along with a number of twisted hypermultiplets. The origin of these twisted hypermultiplets is explained from the four dimensional perspective. We also propose the three dimensional mirror theories for such linear quivers. These provide explicit descriptions of the magnetic quivers of all AD theories in question in terms of quiver diagrams with unitary gauge groups, together with a collection of free hypermultiplets. A number of quiver gauge theories presented in this paper are new and have not been studied elsewhere in the literature.
The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $\mathcal{N}=2$ preserving exactly marginal operators of 3d $S$-fold SCFTs. Two families of such theories are considered: one is constructed by gauging the diagonal flavour symmetry of the $T(U(2))$ and $T(U(3))$ theories, and the other by gauging the diagonal flavour symmetry of the $T^{[2,1^2]}_{[2,1^2]}(SU(4))$ theory. In both families, it is possible to turn on a Chern--Simons level for each gauge group and to couple to each theory various numbers of hypermultiplets. The detailed analysis of the exactly marginal operators, along with the superconformal indices, allows us to determine whether supersymmetry gets enhanced in the infrared and to deduce the amount of supersymmetry of the corresponding SCFT.
We propose some new infra-red dualities for $2d$ $\mathcal{N}=(0,2)$ theories. The first one relates a $USp(2N)$ gauge theory with one antisymmetric chiral, four fundamental chirals and $N$ Fermi singlets to a Landau-Ginzburg model of $N$ Fermi and $6N$ chiral fields with cubic interactions. The second one relates $SU(2)$ linear quiver gauge theories of arbitrary length $N-1$ with the addition of $N$ Fermi singlets for any non-negative integer $N$. They can be understood as a generalization of the duality between an $SU(2)$ gauge theory with four fundamental chirals and a Landau-Ginzburg model of one Fermi and six chirals with a cubic interaction. We derive these dualities from already known $4d$ $\mathcal{N}=1$ dualities by compactifications on $\mathbb{S}^2$ with suitable topological twists and we further test them by matching anomalies and elliptic genera. We also show how to derive them by iterative applications of some more fundamental dualities, in analogy with similar derivations for parent dualities in three and four dimensions.
We construct a family of $4d$ $\mathcal{N}=1$ theories that we call $E^σ_ρ[USp(2N)]$ which exhibit a novel type of $4d$ IR duality very reminiscent of the mirror duality enjoyed by the $3d$ $\mathcal{N}=4$ $T^σ_ρ[SU(N)]$ theories. We obtain the $E^σ_ρ[USp(2N)]$ theories from the recently introduced $E[USp(2N)]$ theory, by following the RG flow initiated by vevs labelled by partitions $ρ$ and $σ$ for two operators transforming in the antisymmetric representations of the $USp(2N) \times USp(2N)$ IR symmetries of the $E[USp(2N)]$ theory. These vevs are the $4d$ uplift of the ones we turn on for the moment maps of $T[SU(N)]$ to trigger the flow to $T^σ_ρ[SU(N)]$. Indeed the $E[USp(2N)]$ theory, upon dimensional reduction and suitable real mass deformations, reduces to the $T[SU(N)]$ theory. In order to study the RG flows triggered by the vevs we develop a new strategy based on the duality webs of the $T[SU(N)]$ and $E[USp(2N)]$ theories.
Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$ in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.
Gauge theories in four dimensions can exhibit interesting low energy phenomena, such as infrared enhancements of global symmetry. We explore a class of 4d N=1 gauge theories arising from a construction that is motivated by duality walls in 5d gauge theories. Their quiver descriptions bear a resemblance to 4d theories obtained by compactifying 6d N=(1,0) superconformal field theories on a torus with fluxes, but with lower number of flavours and different number of gauge singlets and superpotentials. One of the main features of these theories is that they exhibit a flavour symmetry enhancement, and with supersymmetry enhancement for certain models, in the infrared. Properties of the superconformal fixed points of such theories are investigated in detail.
We propose various new 3d N=2 dualities exploiting their recently discovered connection to the duality relations for 2d free field CFT correlators. Most of the dualities involve, as the main building block, a quiver theory with monopole superpotential which enjoys various interesting properties such as being self-dual and reducing, in a suitable real mass deformation, to the familiar T[SU(N)] theory. In particular we propose a duality for the U(N) theory with one adjoint and k+1 fundamental flavors. By iterating some basic dualities we can bring the theory to a stable form which, in turns, allows us to find a dual frame where the rank of the original theory appears as a parameter.
We discuss compactifications of rank $Q$ E-string theory on a torus with fluxes for abelian subgroups of the $E_8$ global symmetry of the $6d$ SCFT. We argue that the theories corresponding to such tori are built from a simple model we denote as $E[USp(2Q)]$. This model has a variety of non trivial properties. In particular the global symmetry is $USp(2Q)\times USp(2Q)\times U(1)^2$ with one of the two $USp(2Q)$ symmetries emerging in the IR as an enhancement of an $SU(2)^Q$ symmetry of the UV Lagrangian. The $E[USp(2Q)]$ model after dimensional reduction to $3d$ and a subsequent Coulomb branch flow is closely related to the familiar $3d$ $T[SU(Q)]$ theory, the model residing on an S-duality domain wall of $4d$ $\mathcal{N}=4$ $SU(Q)$ SYM. Gluing the $E[USp(2Q)]$ models by gauging the $USp(2Q)$ symmetries with proper admixtures of chiral superfields gives rise to systematic constructions of many examples of $4d$ theories with emergent IR symmetries. We support our claims by various checks involving computations of anomalies and supersymmetric partition functions. Many of the needed identities satisfied by the supersymmetric indices follow directly from recent mathematical results obtained by E. Rains.
We investigate the relation between 3d N=2 theories and 2d free field correlators or Dotsenko-Fateev (DF) integrals for Liouville CFT. We show that the S^2xS^1 partition functions of some known 3d Seiberg-like dualities reduce, in a suitable 2d limit, to known basic duality identities for DF correlators. These identities are applied in a variety of contexts in CFT, as for example in the derivation of the DOZZ 3-point function. Reversing the logic, we can try to guess new 3d IR dualities which reduce to more intricate duality relations for the DF correlators. For example, we show that a recently proposed duality relating the U(N) theory with one flavor and one adjoint to a WZ model can be regarded as the 3d ancestor of the evaluation formula for the DF integral representation of the 3-point correlator. We are also able to interpret the analytic continuation in the number of screening charges, which is performed on the CFT side to reconstruct the DOZZ 3-point function, as the geometric transition relating the 3d U(N) theory to the 5d T_2 theory.
S-duality domain walls are extended objects in supersymmetric gauge theories with several rich physical properties. This paper focuses on 3d N=2 gauge theories associated with S-duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours. The theories associated with multiple duality walls are constructed by gluing together a basic building block, which is the theory associated with a single duality wall. We propose the prescription for gluing many copies of such a basic building block together as well as present the prescription for self-gluing. A number of dualities between such theories are discovered and studied using the supersymmetric index. This work generalises the notion of the S-fold theory, which has been so far studied extensively in the context of duality walls in the 4d super-Yang-Mills theory, to the theory with lower amounts of supersymmetry.