Resolving class-S theories
In this dissertation, we discuss methods to resolve various ambiguities that arise in cataloguing class-S theories [1, 2]. We first review some facts about class-S theories. We, then, present two methods to identify product (also referred to as factorized) theories in class-S and apply our results to the E₆ (both twisted and untwisted) sector and the E₇ sector. We also present a possible explanation for the existence of factorization phenomena to the existence of various N = (2, 2) surface defects and study the factorization of the Coulomb branch in such theories. We also present pairs of theories where the conventionally used invariants are not sufficient to distinguish them, and present methods to identify them uniquely. The existence of such pairs is conjectured to exist due to distinct forms of their global symmetry. We also present results for the classification of the last remaining sector for the class-S, namely the nonabelian twisted D₄ sector.