Advancements in Functorial Homological Mirror Symmetry

TL;DR

This paper explores how functorial homological mirror symmetry can be applied to string theory setups, emphasizing the need for further formal development and introducing cobordism techniques for invariant evaluation.

Contribution

It demonstrates the application of functorial homological mirror symmetry to string theory contexts and highlights the importance of cobordism methods for computing invariants.

Findings

Application of functorial HMS to concrete string theory models

Identification of cobordism techniques as crucial tools

Need for further formal development of the framework

Abstract

Mostly inspired by recent work by Katzarkov, Kontsevich, and Sheshmani, combined with previous work by Aganagic, Ooguri, Saulina and Vafa with regard to BPS black hole microstate counting in terms of topological field theory calculations, we will show how these tools can be applied to concrete setups arising from String Theory, and why the formalism of functorial Homological Mirror Symmetry needs to be further developed. A crucial ingredient will turn out being cobordism techniques for evaluating invariants.