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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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1432-0916

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WallCrossing Free Fermions and Crystal Melting

Authors: Piotr Sułkowski
Publish Date: 2010/10/26
Volume: 301, Issue: 2, Pages: 517-562
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Abstract

We describe wallcrossing for local toric CalabiYau manifolds without compact fourcycles in terms of free fermions vertex operators and crystal melting Firstly to each such manifold we associate two states in the free fermion Hilbert space The overlap of these states reproduces the BPS partition function corresponding to the noncommutative DonaldsonThomas invariants given by the modulus square of the topological string partition function Secondly we introduce the wallcrossing operators which represent crossing the walls of marginal stability associated to changes of the Bfield through each twocycle in the manifold BPS partition functions in nontrivial chambers are given by the expectation values of these operators Thirdly we discuss crystal interpretation of such correlators for this whole class of manifolds We describe evolution of these crystals upon a change of the moduli and find crystal interpretation of the flop transition and the DT/PT transition The crystals which we find generalize and unify various other CalabiYau crystal models which appeared in literature in recent yearsI thank Jim Bryan for discussions which inspired this project I am also grateful to Robbert Dijkgraaf Albrecht Klemm Hirosi Ooguri Yan Soibelman Balazs Szendroi Cumrun Vafa and Masahito Yamazaki for useful conversations I appreciate the hospitality and inspiring atmosphere of the Focus Week on New Invariants and Wall Crossing organized at IPMU in Tokyo International Workshop on Mirror Symmetry organized at the University of Bonn and 7 th Simons Workshop on Mathematics and Physics as well as the High Energy Theory Group at Harvard University This research was supported by the DOE grant DEFG0392ER40701FG02 the Humboldt Fellowship the Foundation for Polish Science and the European Commission under the MarieCurie International Outgoing Fellowship Programme The contents of this publication reflect only the views of the author and not the views of the European CommissionThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team

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