Heriot-Watt Mathematics Report Series
HWM05-22, 28 Oct 2005
Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
N Caporaso, M Cirafici, L Griguolo, S Pasquetti, D Seminara and R J Szabo
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
$\PP^1$. 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.
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