English

Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities

High Energy Physics - Theory 2015-06-15 v1 Algebraic Geometry Combinatorics

Abstract

We construct a two-dimensional crystal melting model which reproduces the BPS index of D2-D0 states bound to a non-compact D4-brane on an arbitrary toric Calabi-Yau singularity. The crystalline structure depends on the toric divisor wrapped by the D4-brane. The molten crystals are in one-to-one correspondence with the torus fixed points of the moduli space of the quiver gauge theory on D-branes. The F- and D-term constraints of the gauge theory are regarded as a generalization of the ADHM constraints on instantons. We also show in several examples that our model is consistent with the wall-crossing formula for the BPS index.

Keywords

Cite

@article{arxiv.1304.6724,
  title  = {Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities},
  author = {Takahiro Nishinaka and Satoshi Yamaguchi and Yutaka Yoshida},
  journal= {arXiv preprint arXiv:1304.6724},
  year   = {2015}
}

Comments

72 pages, 44 figures