Supersymmetric Proof of the Hirzebruch-Riemann-Roch Theorem for Non-K\"ahler Manifolds

TL;DR

This paper provides a supersymmetric quantum mechanical proof of the Hirzebruch-Riemann-Roch theorem applicable to general complex compact manifolds, extending its validity beyond Kähler cases.

Contribution

It introduces a novel supersymmetric approach to prove the HRR theorem for non-Kähler manifolds, broadening the theorem's applicability.

Findings

Validated the HRR theorem for non-Kähler manifolds using supersymmetric quantum mechanics

Connected topological invariants with supersymmetric functional integrals

Extended the proof techniques beyond traditional geometric methods

Abstract

We present the proof of the HRR theorem for a generic complex compact manifold by evaluating the functional integral for the Witten index of the appropriate supersymmetric quantum mechanical system.