(2,0) theory on circle fibrations

We consider (2, 0) theory on a manifold M6 that is a fibration of a spatial S1 over some five-dimensional base manifold M5. 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 M6 the low energy effective theory obtained through dimensional reduction on the circle is a Maxwell theory on M5. The parameters describing the local geometry of the fibration are interpreted respectively as the metric on M5, 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 M5. Completing the theory with Yukawa and ϕ4 terms, and suitably modifying the supersymmetry transformations, we obtain a supersymmetric Yang-Mills theory which includes terms related to the geometry of the fibration.