Topological Sigma B Model in 4-Dimensions

TL;DR

This paper introduces a 4-dimensional topological sigma B-model that maps 4-manifolds to Calabi-Yau spaces, potentially leading to new invariants of 4-manifolds based on complex structures.

Contribution

It develops a novel 4D topological field theory extending sigma models, dependent on complex structures but independent of metrics, and explores its implications for 4-manifold invariants.

Findings

Defines a 4D topological sigma B-model with Calabi-Yau targets

Shows independence from Riemannian metric of the source manifold

Suggests potential for new smooth invariants of 4-manifolds

Abstract

We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensiona topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.