Crystal melting on toric surfaces

Michele Cirafici; Amir Kian Kashani-Poor; Richard J. Szabo

doi:10.1016/j.geomphys.2011.06.014

Crystal melting on toric surfaces

Michele Cirafici, Amir Kian Kashani-Poor^*, Richard J. Szabo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2199-2218
Number of pages	20
Journal	Journal of Geometry and Physics
Volume	61
Issue number	11
DOIs	https://doi.org/10.1016/j.geomphys.2011.06.014
Publication status	Published - Nov 2011

Keywords

Counting of subschemes
Diagrammatic techniques
Instanton counting in N=4 gauge theory
Toric surfaces

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/j.geomphys.2011.06.014

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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.",

keywords = "Counting of subschemes, Diagrammatic techniques, Instanton counting in N=4 gauge theory, Toric surfaces",

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AU - Cirafici, Michele

AU - Kashani-Poor, Amir Kian

AU - Szabo, Richard J.

PY - 2011/11

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N2 - 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.

AB - 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.

KW - Counting of subschemes

KW - Diagrammatic techniques

KW - Instanton counting in N=4 gauge theory

KW - Toric surfaces

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U2 - 10.1016/j.geomphys.2011.06.014

DO - 10.1016/j.geomphys.2011.06.014

M3 - Article

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VL - 61

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EP - 2218

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 11

ER -

Crystal melting on toric surfaces

Abstract

Keywords

ASJC Scopus subject areas

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