Gauge theory and mirror symmetry

Understand

Outlined in this paper is a description of \emph{equivariance} in the world of 2-dimensional extended topological quantum field theories, under a topological action of compactLie groups.

• In physics language, I am gauging the theories --- coupling them to a principal bundle on the surface world-sheet.
• I describe the data needed to gauge the theory, as well as the computation of the gauged theory, the result of integrating over all bundles.
• The relevant theories are A-models, such as arise from the Gromov-Witten theory of a symplectic manifold with Hamiltonian group action, and the mathematical description starts with a group action on the generating category (the Fukaya category, in this example) which is factored through the topology of the group.