Crystal melting on toric surfaces
arXiv:0912.0737 · doi:10.1016/j.geomphys.2011.06.014
Abstract
We study the relationship between the statistical mechanics of crystal melting and instanton counting in N=4 supersymmetric U(1) gauge theory on toric surfaces. We argue that, in contrast to their six-dimensional cousins, the two problems are related but not identical. We develop a vertex formalism for the crystal partition function, which calculates a generating function for the dimension 0 and 1 subschemes of the toric surface, and describe the modifications required to obtain the corresponding gauge theory partition function.
30 pages; v2: references added
References in corpus (8)
- Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
- Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
- The Nekrasov Conjecture for Toric Surfaces
- Instantons on ALE spaces and orbifold partitions
- Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces
- Instanton on toric singularities and black hole countings
- Hilbert schemes and stable pairs: GIT and derived category wall crossings
- Poincare invariants
Cited by in corpus (10)
- N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
- N=2 quiver gauge theories on A-type ALE spaces
- Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
- Neurons on Amoebae
- N=2 gauge theories, instanton moduli spaces and geometric representation theory
- Noncommutative Instantons in Diverse Dimensions
- Quivers, Line Defects and Framed BPS Invariants
- Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
- On Framed Quivers, BPS Invariants and Defects
- Quantum Black Holes, Elliptic Genera and Spectral Partition Functions