Superconformal Theories in Six Dimensions

TL;DR

This thesis explores superconformal symmetry in six dimensions, focusing on the (2,0) theory, its origins, compactifications, and the formalism for manifest superconformal invariance, including tensor multiplets and self-dual strings.

Contribution

It develops a formalism for manifest superconformal invariance in six-dimensional (2,0) theories and analyzes their origins and compactifications from string and M-theory.

Findings

Formalism for superconformal symmetry in 6D established

Connections between (2,0) theory and string/M-theory clarified

Coupling of self-dual strings to tensor multiplets achieved

Abstract

This thesis consists of an introductory text, which is divided into two parts, and six appended research papers. The first part contains a general discussion on conformal and superconformal symmetry in six dimensions, and treats how the corresponding transformations act on space-time and superspace fields. We specialize to the case with chiral (2,0) supersymmetry. A formalism is presented for incorporating these symmetries in a manifest way. The second part of the thesis concerns the so called (2,0) theory in six dimensions. The different origins of this theory in terms of higher-dimensional theories (Type IIB string theory and M-theory) are treated, as well as compactifications of the six-dimensional theory to supersymmetric Yang-Mills theories in five and four space-time dimensions. The free (2,0) tensor multiplet field theory is introduced and discussed, and we present a formalism in which its superconformal covariance is made manifest. We also introduce a tensile self-dual string and discuss how to couple this string to the tensor multiplet fields in a way that respects superconformal invariance.