Topological String Partition Function on Noncommutative Resolutions

Abstract: This talk focuses on the Gopakumar-Vafa invariants of noncommutative resolutions of compact Calabi-Yau threefolds with conifolds which do not admit a Kahler small resolution. I present and give evidence for a proposal for computing these GV invariants using the enumerative geometry of all small resolutions considered simultaneously. The "Kahler" moduli space of any small resolution X splits into disjoint copies corresponding to fractional B-fields along the exceptional P^1s and indexed by the torsion subgroup of H^3(X,Z). In this way, we get multiple large radius limits, leading to multiple partition functions, all determined by the Gopakumar-Vafa invariants. The partition functions can be computed in many cases by B-model techniques on different mirrors corresponding to different choices of the fractional B-field. The main example discussed in this talk is Kuznetsov's noncommutative resolution of the double cover of P^3 branched along a degree 8 determinantal hypersurface. Many of the GV invariants deduced from the B-model partition functions can be confirmed by enumerative geometry of the small resolutions after showing that the exceptional P^1's all represent 2-torsion classes in H_2(X,Z). This talk is based on joint work in progress with Albrecht Klemm, Thorsten Schimannek, and Eric Sharpe.

HEP - theorymathematical physics

Audience: researchers in the topic

QFT and Geometry

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