Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory

Nicola Caporaso, Michele Cirafici, Luca Griguolo, Sara Pasquetti, Domenico Seminara, Richard J. Szabo

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19 Citations (Scopus)

Abstract

We continue our study of the large N phase transition in q-deformed Yang-Mills theory on the sphere and its role in connecting topological strings to black hole entropy. We study in detail the chiral theory defined in terms of uncoupled single U(N) representations at large N and write down the resulting partition function by means of the topological vertex. The emergent toric geometry has three Kähler parameters, one of which corresponds to the expected fibration over double-struck P sign1. By taking a suitable double-scaling limit we recover the chiral Gross-Taylor string expansion. To analyse the phase transition we construct a matrix model which describes the chiral gauge theory. It has three distinct phases, one of which should be described by the closed topological string expansion. We verify this expectation by explicit comparison between the matrix model and the chiral topological string free energies. We also show that the critical point in the pertinent phase of the matrix model corresponds to a divergence of the topological string perturbation series. © SISSA 2006.

Original languageEnglish
Pages (from-to)865-915
Number of pages51
JournalJournal of High Energy Physics
Issue number1
DOIs
Publication statusPublished - 2006

Keywords

  • Brane Dynamics in Gauge Theories
  • Field Theories in Lower Dimensions
  • Nonperturbative Effects
  • Topological Strings

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