4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations

Abstract

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 $T^{-1}ST=S^{-1}TS$ 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.

arXiv comment58 pages, 18 figures; v2: references added; v3: version published on JHEP

References in corpus (35)

• An Index for 4 dimensional Super Conformal Theories
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Mirror Symmetry in Three Dimensional Gauge Theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• The Exact Superconformal R-Symmetry Extremizes Z
• Comments on String Dynamics in Six Dimensions
• SUSY Gauge Theories on Squashed Three-Spheres
• Notes on SUSY Gauge Theories on Three-Sphere
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• 3d dualities from 4d dualities
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• IR Duality in d=3 N=2 Supersymmetric USp(2N_c) and U(N_c) Gauge Theories
• Exact Superpotentials, Quantum Vacua and Duality in Supersymmetric SP(N_c) Gauge Theories
• Bootstrapping the superconformal index with surface defects
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• 3d dualities from 4d dualities for orthogonal groups
• From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
• E-String Theory on Riemann Surfaces
• 3d Partition Function as Overlap of Wavefunctions
• 3D-partition functions on the sphere: exact evaluation and mirror symmetry
• The supersymmetric index in four dimensions
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Rank $Q$ E-string on a torus with flux
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• New aspects of Argyres--Douglas theories and their dimensional reduction
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• From 3d dualities to 2d free field correlators and back
• Multipoint correlation functions in Liouville field theory and minimal Liouville gravity
• 3d dualities from 2d free field correlators: recombination and rank stabilization
• Boundary Liouville theory at c=1
• Vanishing superconformal indices and the chiral symmetry breaking
• Symmetry enhancement and duality walls in 5d gauge theories

Cited by in corpus (10)

• Higgs, Coulomb, and Hall-Littlewood
• Dualities from dualities: the sequential deconfinement technique
• Rethinking mirror symmetry as a local duality on fields
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• S-confinements from deconfinements
• Monopole deformations of 3d Seiberg-like dualities with adjoint matters
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Dualities and loops on squashed $S^3$
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories
• Sequential deconfinement and self-dualities in $4d$ $\mathcal{N}=1$ gauge theories