Moduli spaces of gauge theories from dimer models: Proof of the correspondence

Franco, Sebastian; Vegh, David

doi:10.1088/1126-6708/2006/11/054

Moduli spaces of gauge theories from dimer models: Proof of the correspondence

Franco, Sebastian; Vegh, David

Authors

Sebastian Franco

David Vegh

Abstract

Recently, a new way of deriving the moduli space of quiver gauge theories that arise on the world–volume of D3–branes probing singular toric Calabi–Yau cones was conjectured. According to the proposal, the gauge group, matter content and tree–level superpotential of the gauge theory is encoded in a periodic tiling, the dimer graph. The conjecture provides a simple procedure for determining the moduli space of the gauge theory in terms of perfect matchings. For gauge theories described by periodic quivers that can be embedded on a two–dimensional torus, we prove the equivalence between the determination of the toric moduli space with a gauged linear sigma model and the computation of the Newton polygon of the characteristic polynomial of the dimer model. We show that perfect matchings are in one–to–one correspondence with fields in the linear sigma model. Furthermore, we prove that the position in the toric diagram of every sigma model field is given by the slope of the height function of the corresponding perfect matching.

Citation

Franco, S., & Vegh, D. (2006). Moduli spaces of gauge theories from dimer models: Proof of the correspondence. Journal of High Energy Physics, 2006(11), Article 054. https://doi.org/10.1088/1126-6708/2006/11/054

Journal Article Type	Article
Publication Date	Nov 21, 2006
Deposit Date	Jan 27, 2014
Publicly Available Date	Feb 14, 2014
Journal	Journal of High Energy Physics
Print ISSN	1126-6708
Electronic ISSN	1029-8479
Publisher	Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed	Peer Reviewed
Volume	2006
Issue	11
Article Number	054
DOI	https://doi.org/10.1088/1126-6708/2006/11/054
Keywords	AdS-CFT and dS-CFT Correspondence, Brane Dynamics in Gauge Theories.