Surface operators, Seiberg-dual quivers and contours[HBNI Th176]

Abstract

In this thesis, we study surface operators in N = 2 supersymmetric QCD theories with gauge group SU(N) and 2N fundamental flavours in four dimensions . The matter content of the theory ensures that it is conformal in the limit that the flavour masses are zero and is referred to as asymptotically conformal SQCD. The low energy physics of the gauge theory on the Coulomb branch in the presence of the defect is described by two holomorphic functions, the prepotential and the twisted chiral superpotential. While the prepotential describes the effective four dimensional theory in the absence of a defect, the twisted chiral superpotential describes the effective theory on the defect. So, our focus will be on computing the twisted superpotential and analysing it. We study surface operators following two different approaches, namely as monodromy defects and flavor defects. Our goal is to clarify the relationship between these different approaches of surface operators. In addition, we want to clarify Seiberg duality in the context of surface operators in N = 2 SQCD. We also study modular properties of simplest possible surface operator in four dimensional N = 2 SQCD with gauge group SU(2) and four fundamental flavours It is well known that this theory enjoys S-duality. Using the constraints imposed by the S-duality, we show that the instanton contribution to the twisted chiral superpotential can be resummed into elliptic functions and (quasi-) modular forms of the duality group.