TY - JOUR

T1 - Topological strings and large N phase transitions II

T2 - Chiral expansion of q-deformed Yang-Mills theory

AU - Caporaso, Nicola

AU - Cirafici, Michele

AU - Griguolo, Luca

AU - Pasquetti, Sara

AU - Seminara, Domenico

AU - Szabo, Richard J.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Brane Dynamics in Gauge Theories

KW - Field Theories in Lower Dimensions

KW - Nonperturbative Effects

KW - Topological Strings

UR - http://www.scopus.com/inward/record.url?scp=33645506635&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2006/01/036

DO - 10.1088/1126-6708/2006/01/036

M3 - Article

SP - 865

EP - 915

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

ER -