Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow

We study the 't Hooft anomalies of four-dimensional superconformal field theories that arise from M5-branes wrapped on a punctured Riemann surface. In general there are two independent contributions to the anomalies. There is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface; this contribution knows about the punctures only through its dependence on the Euler characteristic of the surface. The second set of contributions comes from local data at the punctures; these terms are independent from the bulk data of the surface. Using anomaly inflow in M-theory, we describe the general structure of the anomalies for cases when the four-dimensional theories preserve N=2 supersymmetry. We additionally discuss the anomalies corresponding to (p,q) punctures in N=1 theories.Comment: version 2, 38 pages. We simplified the discussion of the inflow procedure with punctures and removed the details of the explicit computation of the puncture anomalies in order to focus on arguing the main new ideas. Added clarification on main resul

Dimensionally reducing generalized symmetries from (3+1)-dimensions

Recently there has been an increasing interest in the study of generalized symmetries in dimensions higher than two. This has lead to the discovery of various manifestations of generalized symmetries, notably higher-group and non-invertible symmetries, in four dimensions. In this paper we shall examine what happens to this structure when the 4d theory is compactified to lower dimensions, specifically to 3d and 2d, where we shall be mainly interested in generalized symmetry structures whose origin can be linked to mixed flavor-gauge anomalies. We discuss several aspects of the compactification, and in particular argue that under certain conditions the discussed generalized symmetry structure may trivialize in the infrared. Nevertheless, we show that even when this happens the presence of the 4d generalized symmetry structure may still leave an imprint on the low-energy theory in terms of additional ’t Hooft anomalies or by breaking part of the symmetry. We apply and illustrate this using known examples of compactifications from four dimensions, particularly, the reduction of 4d N = 1 U(Nc) SQCD on a circle to 3d and on a sphere to 2d

Emily Nardoni - From Seiberg-Witten Theory to Adjoint QCD

Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions ("adjoint QCD") flows to a phase with confinement and chiral symmetry breaking. In this talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of a renormalization group flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry-breaking mass for its adjoint scalars. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the supersymmetry-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.     String Seminars: https://cern.zoom.us/j/61053603623?pwd=THhlNnU4ZXljQjFxMjVwQlVxVHdQZz0

Aspects of Supersymmetric Conformal Field Theories in Various Dimensions

In this dissertation we study properties of superconformal field theories (SCFTs) that arise from a variety of constructions. We begin with an extended review of various techniques in supersymmetry that are relevant throughout the work. In Chapter 3, we discuss aspects of theories with superpotentials given by Arnold's A,D,E singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional N = 1 variants of supersymmetric QCD, with U( Nc) or SU(Nc) gauge group, Nf fundamental flavors, and adjoint matter fields X and Y appearing in WA,D,E(X,Y) superpotentials. We explore these issues by considering various deformations of the WA,D,E superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional N = 1 supersymmetric SU(2) gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the N = 2 Argyres-Douglas theory H0, and a further deformation to an N = 1 SCFT with low a central charge. Then for the latter half of the dissertation we turn our attention to 4d SCFTs that arise from compactifications of M5-branes. In Chapter 6, we field-theoretically construct 4d N = 1 quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus g and n punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees p and q. In Chapter 7, we study the 't Hooft anomalies of the SCFTs that arise from these compactifications. In general there are two independent contributions to the anomalies: there is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface, and there is a set of contributions due to local data at the punctures. Using anomaly inflow in M-theory, we describe how this general structure arises for cases when the four-dimensional theories preserve N = 2 supersymmetry, and derive terms that account for the local data at the punctures

Dualities of adjoint SQCD and supersymmetry enhancement

Abstract We propose a new dual description of four-dimensional N $$\mathcal{N}$$ = 1 SU(N) gauge theory with one adjoint (X) and N f fundamental matters with a superpotential W = TrX p+1. The dual theory consists of the D $$\mathcal{D}$$ p [SU(N)] Argyres-Douglas theory coupled to SU(N) gauge theory and N f fundamentals with a superpotential deformation. We study renormalization group fixed points of the Argyres-Douglas dual theories with and without superpotential deformations, and identify the conditions for them to be dual to the fixed points of adjoint SQCD. We check our proposal via matching central charges, chiral operators and superconformal indices. We find that when N f = 2N and p = 2, the dual theory flows to N $$\mathcal{N}$$ = 2 SU(N) superconformal QCD with 2N flavors upon suitable superpotential deformation, exhibiting supersymmetry enhancement

Class S\mathcal{S} Anomalies from M-theory Inflow

International audienceWe present a first principles derivation of the anomaly polynomials of 4d N=2 class S theories of type AN-1 with arbitrary regular punctures, using anomaly inflow in the corresponding M-theory setup with N M5-branes wrapping a punctured Riemann surface. The labeling of punctures in our approach follows entirely from the analysis of the 11d geometry and G4 flux. We highlight the applications of the inflow method to the AdS/CFT correspondence