Quantization of topological-holomorphic field theories: local aspects

Abstract

In both mathematics and physics, topological field theories and holomorphic field theories appear naturally, but there are interesting theories that are hybrids -- looking topological in some directions and holomorphic in others -- such as twists of supersymmetric field theories or Costello's 4-dimensional Chern--Simons theory. In this paper we construct perturbative, one-loop quantizations rigorously on the model manifold ${\mathbb{R}}^m\times {\mathbb{C}}^n$, and find a remarkable vanishing result about anomalies: the one-loop obstruction to quantization on ${\mathbb{R}}^m\times {\mathbb{C}}^n$ vanishes when $m\ge 1$. A concrete consequence of our results is the existence of exact and finite quantizations at one-loop for twists of pure $\mathcal{N}=2$ four-dimensional supersymmetric Yang--Mills theory.

Cited by in corpus (1)

• Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions