Advances in Theoretical and Mathematical Physics

Volume 18 (2014)

Number 6

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

Pages: 1369 – 1436

DOI: http://dx.doi.org/10.4310/ATMP.2014.v18.n6.a5

Authors

Nicolas M. Addington (Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)

Edward P. Segal (Department of Mathematics, Imperial College, London, United Kingdom)

Eric R. Sharpe (Department of Physics, Virginia Polytechnic Institute, Blacksburg, Virginia, U.S.A.)

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.

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