Higher gauge theory, self-dual strings and 6D superconformal field theory

Abstract

We present two explicit constructions in higher gauge theory of relevance to string and M-theory: the non-abelian self-dual string and a six-dimensional (1,0) super conformal field theory. We start by outlining higher gauge theory from the point of view of morphisms of graded differential algebras and extend this to generalized higher gauge theory. We discuss two models of the string Lie 2-algebra and give twisted versions of these that are suitable for our non-abelian constructions. We argue from analogy to monopoles that the string Lie 2-algebra is the relevant higher gauge structure for the non-abelian generalization of the self-dual string. We show that the twisted versions can be used to write down consistent non-abelian self-dual string equations. Moreover, we give the elementary solution, which passes the relevant consistency checks. We also use this gauge structure to present an action for a six-dimensional super conformal field theory containing a non-abelian tensor multiplet based on ingredients available in the literature. The resulting (1,0)-model contains the field content of the (2,0)-theory, allows for a self-dual three-form curvature and straightforwardly reduces to a four-dimensional supersymmetric Yang–Mills theory. It can be regarded as a stepping stone towards a potential construction of the (2,0)-theory.