On quantization of singular varieties and applications to D-branes

TL;DR

This paper computes differential operators on certain singular varieties, linking algebraic geometry with D-brane physics in string theory, and showing that these operators reflect the singularities' geometry without resolution.

Contribution

It provides explicit calculations of differential operator rings on singular varieties, supporting their role in modeling D-branes in string theory.

Findings

Differential operator rings match string theory predictions.

Results do not depend on resolution of singularities.

Supports geometric interpretation of D-branes on singular spaces.

Abstract

We calculate the ring of differential operators on some singular affine varieties (intersecting stacks, a point on a singular curve or an orbifold). Our results support the proposed connection of the ring of differential operators with geometry of D-branes in (bosonic) string theory. In particular, the answer does know about the resolution of singularities in accordance with the string theory predictions.