Flat gauge fields and the Riemann-Hilbert correspondence

TL;DR

This paper explores the geometric phase in quantum physics through Deligne's Riemann-Hilbert correspondence and extends flat gauge fields to B-branes, linking gauge theory with algebraic geometry.

Contribution

It introduces a novel interpretation of the geometric phase using the Riemann-Hilbert correspondence and generalizes flat gauge fields to B-branes as holonomic D-modules.

Findings

Interpreted the Aharonov-Bohm effect via Riemann-Hilbert correspondence

Extended flat gauge fields to B-branes as D-modules

Connected gauge theory concepts with algebraic geometry frameworks

Abstract

The geometric phase that appears in the effects of Aharonov-Bohm type is interpreted in the frame of Deligne's version of the Riemann-Hilbert correspondence. We extend also the concept of flat gauge field to $B$-branes which are coherent sheaves, so that such a field on a sheaf turns it into a holonomic regular $D$-module.