Regularizing Calabi-Yau topological conformal field theories using cutoff heat kernels

TL;DR

This paper develops a method to regularize Calabi-Yau topological conformal field theories by modifying heat kernels and demonstrates the equivalence of two regularization approaches, linking different cutoff schemes.

Contribution

It introduces a novel regularization technique for Calabi-Yau TCFTs using eigenspace restrictions of the Laplacian, establishing their equivalence and relations between cutoff schemes.

Findings

Two distinct regularization methods are shown to be equivalent.

Regularized TCFTs are related across different cutoff parameters.

The approach connects heat kernel modifications with Calabi-Yau geometry.

Abstract

In this paper we construct a family of topological conformal field theories (TCFTs) associated to a Calabi-Yau space by modifying the heat kernel and sections of the Calabi-Yau space. This is done by restricting to certain eigenspaces of the Laplacian. We then present two a-priori distinct ways to regularize the Calabi-Yau TCFT by using these modified heat kernels, and then show that they are equivalent. Finally, we relate the regularized TCFTs for different cutoffs.