Black holes, instanton counting on toric singularities and q-deformed two-dimensional Yang-Mills theory

Luca Griguolo, Domenico Seminara, Richard J. Szabo, Alessandro Tanzini

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

We study the relationship between instanton counting in N = 4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the known instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces. © 2007 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalNuclear Physics B
Volume772
Issue number1-2
DOIs
Publication statusPublished - 11 Jun 2007

Keywords

  • Black holes
  • Brane dynamics in gauge theories
  • Chern-Simons theories
  • Field theories in lower dimensions
  • Solitons monopoles and instantons

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