Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-10-29
Commun. Math. Phys.301:517-562, 2011
Physics
High Energy Physics
High Energy Physics - Theory
61 pages, 14 figures, published version
Scientific paper
10.1007/s00220-010-1153-1
We describe wall-crossing for local, toric Calabi-Yau manifolds without compact four-cycles, 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 non-commutative Donaldson-Thomas invariants, given by the modulus square of the topological string partition function. Secondly, we introduce the wall-crossing operators which represent crossing the walls of marginal stability associated to changes of the B-field through each two-cycle in the manifold. BPS partition functions in non-trivial 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 Calabi-Yau crystal models which appeared in literature in recent years.
No associations
LandOfFree
Wall-crossing, free fermions and crystal melting does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Wall-crossing, free fermions and crystal melting, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wall-crossing, free fermions and crystal melting will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-403994