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

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 a non-Kähler small resolution of a singular Calabi-Yau. We conjecture that such non-Kähler resolutions are typical in D-brane probes of such theories.