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.