Balanced Topological Field Theories

TL;DR

Balanced topological field theories are a new class of theories linked to moduli problems with zero virtual dimension, computing Euler characteristics and connecting to Morse theory and twisted sigma-models.

Contribution

Introduction of balanced topological field theories associated with moduli problems, their relation to iterated superspaces, and the derivation of a general action defining Morse theory on field space.

Findings

Theories compute Euler characteristics of moduli spaces.

Most general action relates to Morse theory on field space.

Examples include relations to topological sigma-models.

Abstract

We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.