(2,0) theory on circle fibrations

TL;DR

This paper explores the dimensional reduction of (2,0) theory on circle fibrations, deriving a Maxwell theory on the base manifold and extending it to a supersymmetric Yang-Mills theory incorporating geometric effects.

Contribution

It provides a detailed derivation of the Maxwell and supersymmetric Yang-Mills theories from (2,0) theory on circle fibrations, including geometric parameters and symmetries.

Findings

Derived the Maxwell theory action from (2,0) theory on circle fibrations.

Extended to a supersymmetric Yang-Mills theory with geometric terms.

Analyzed symmetries originating from six-dimensional superconformal symmetry.

Abstract

We consider (2,0) theory on a manifold M_6 that is a fibration of a spatial S^1 over some five-dimensional base manifold M_5. Initially, we study the free (2,0) tensor multiplet which can be described in terms of classical equations of motion in six dimensions. Given a metric on M_6 the low energy effective theory obtained through dimensional reduction on the circle is a Maxwell theory on M_5. The parameters describing the local geometry of the fibration are interpreted respectively as the metric on M_5, a non-dynamical U(1) gauge field and the coupling strength of the resulting low energy Maxwell theory. We derive the general form of the action of the Maxwell theory by integrating the reduced equations of motion, and consider the symmetries of this theory originating from the superconformal symmetry in six dimensions. Subsequently, we consider a non-abelian generalization of the Maxwell theory on M_5. Completing the theory with Yukawa and phi^4 terms, and suitably modifying the supersymmetry transformations, we obtain a supersymmetric Yang-Mills theory which includes terms related to the geometry of the fibration.