Gauge Theory in higher dimensions, II

TL;DR

This paper aims to develop a Floer theory for Calabi-Yau 3-folds, extending the holomorphic Casson invariant, and discusses deformation and compactness issues related to gauge fields and submanifolds in manifolds with exceptional holonomy.

Contribution

It introduces a formal framework for Floer theory in higher-dimensional gauge theories, extending existing invariants to Calabi-Yau 3-folds and discussing deformation and compactness challenges.

Findings

Proposes a formal Floer theory for Calabi-Yau 3-folds.

Discusses deformation of gauge equations and submanifolds.

Addresses compactness issues in moduli spaces of G2-instantons.

Abstract

The main aim of the paper is to develop the "Floer theory" associated to Calabi-Yau 3-folds, exending the analogy of Thomas' "holomorphic Casson invariant". The treatment in the body of the paper is largely formal, assuming appropriate compactness properties of moduli spaces of $G_{2}$-instantons, but in the last section we make some remarks about these compactness isssues. Section 3 of the paper contains a general dscussion of deformations of the equations, for gauge field and submanifolds, associated to manifolds with exceptional holonomy.