Abstract: We consider on one hand the possibility that a supersymmetric N = 1 conformal gauge theory has a strongly coupled locus on the conformal manifold at which a different, dual, conformal gauge theory becomes a good weakly coupled description. On the other hand we discuss the possibility that strongly coupled theories, e.g. SCFTs in class S, having exactly marginal N = 1 deformations admit a weakly coupled gauge theory description on some locus of the conformal manifold. We present a simple algorithm to search for such dualities and discuss several concrete examples. In particular we find conformal duals for N = 1 SQCD models with G2 gauge group and a model with SU(4) gauge group in terms of simple quiver gauge theories. We also find conformal weakly coupled quiver theory duals for a variety of class S theories: T4, R0,4, R2,5, and rank 2n Minahan-Nemeschansky E6 theories. Finally we derive conformal Lagrangians for four dimensional theories obtained by compactifying the E-string on genus g > 1 surface with zero flux. The pairs of dual Lagrangians at the weakly coupled loci have different symmetries which are broken on a general point of the conformal manifold. We match the dimensions of the conformal manifolds, symmetries on the generic locus of the conformal manifold, anomalies, and supersymmetric indices. The simplicity of the procedure suggests that such dualities are ubiquitous.
2:00pm Thesis Defense: Apratim Chakraborty - Invariants of transverse and annular links in combinatorial link Floer homology Where: Math Tower 5-127When: Mon, Jul 29 2:00pm — 3:00pm Title: Invariants of transverse and annular links in combinatorial link Floer homology Speaker: Apratim Chakraborty [Stony Brook University]
Abstract: In this dissertation, we explore the Ozsvath-Szabo-Thurston transverse invariant and various concordance invariants that could be defined using combinatorial link Floer homology. We prove that non-vanishing of the transverse invariant for a link is equivalent to non-vanishing of the invariant for certain transverse cables of that link. As an application, to these results we generate many infinite families of examples of Legendrian and transversely non-simple topological link types. Then, we give a refinement of the transverse invariant. Finally, we define an annular concordance invariant and study its properties. When specialized to braids, this invariant gives bounds on band rank. We also study the relationship of this invariant with transverse and braid monodromy properties. View Details