Calabi-Yau structures on categories of matrix factorizations

TL;DR

This paper explicitly constructs proper Calabi-Yau structures on categories of matrix factorizations, involving formulas with the Kapustin-Li trace and higher corrections, advancing understanding of their cyclic cocycles.

Contribution

It provides explicit formulas for Calabi-Yau structures on matrix factorizations, including higher corrections, which was not previously detailed.

Findings

Explicit proper Calabi-Yau structures derived

Formulas involve Kapustin-Li trace and higher corrections

Enhances understanding of cyclic cocycles on matrix factorizations

Abstract

We write out explicit proper Calabi-Yau structures, i. e. non-degenerate cyclic cocycles on the differential graded categories of matrix factorizations of regular functions with isolated critical points. The formulas involve the Kapustin-Li trace and its "higher corrections".