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December 2014 D-brane probes, branched double covers, and noncommutative resolutions
Nicolas M. Addington, Edward P. Segal, Eric R. Sharpe
Adv. Theor. Math. Phys. 18(6): 1369-1436 (December 2014).


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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Nicolas M. Addington. Edward P. Segal. Eric R. Sharpe. "D-brane probes, branched double covers, and noncommutative resolutions." Adv. Theor. Math. Phys. 18 (6) 1369 - 1436, December 2014.


Published: December 2014
First available in Project Euclid: 4 December 2014

zbMATH: 1311.81202
MathSciNet: MR3285612

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 6 • December 2014
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