D-brane probes, branched double covers, and noncommutative resolutions

TL;DR

This paper investigates D-brane probes in theories from abelian GLSMs, revealing how they perceive branched double covers and noncommutative resolutions, thus connecting physical models with complex geometric and noncommutative structures.

Contribution

It demonstrates how D-brane probes can recover geometric and noncommutative structures in GLSM-derived theories using matrix factorizations, extending understanding of IR limits.

Findings

D-brane probes recover branched double cover structures

Verification of previous results on smooth branched double covers

Proposal that non-Kahler small resolutions are common in such probes

Abstract

This paper describes D-brane probes of theories arising in abelian gauged linear sigma models (GLSMs) describing branched double covers and noncommutative resolutions thereof, via nonperturbative effects rather than as the critical locus of a superpotential. As these theories can be described as IR limits of Landau-Ginzburg models, technically this paper is an exercise in utilizing (sheafy) matrix factorizations. For Landau-Ginzburg models which are believed to flow in the IR to smooth branched double covers, our D-brane probes recover the structure of the branched double cover (and flat nontrivial B fields), verifying previous results. In addition to smooth branched double covers, the same class of Landau-Ginzburg models is also believed to sometimes flow to `noncommutative resolutions' of singular spaces. These noncommutative resolutions are abstract conformal field theories without a global geometric description, but D-brane probes perceive them as non-Kahler small resolutions of a singular Calabi-Yau. We conjecture that such non-Kahler small resolutions are typical in D-brane probes of such theories.