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

Caporaso, N, Cirafici, M, Griguolo, L, Pasquetti, S, Seminara, D and Szabo, RJ (2006) Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory JHEP, 0601. pp. 797-863.

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Abstract

We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point all non-trivial vacua contribute, instantons are enhanced and the theory appears to undergo a phase transition into a strong coupling regime. We rederive these results by performing a saddle-point approximation to the exact partition function. We obtain a q-deformed version of the Douglas-Kazakov equation for two-dimensional Yang-Mills theory on the sphere, whose one-cut solution below the transition point reproduces the resolved conifold geometry. Above the critical point we propose a two-cut solution that should reproduce the chiral-antichiral dynamics found for black holes on the Calabi-Yau threefold and the Gross-Taylor string in the undeformed limit.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Caporaso, NUNSPECIFIEDUNSPECIFIED
Cirafici, MUNSPECIFIEDUNSPECIFIED
Griguolo, LUNSPECIFIEDUNSPECIFIED
Pasquetti, SUNSPECIFIEDUNSPECIFIED
Seminara, DUNSPECIFIEDUNSPECIFIED
Szabo, RJUNSPECIFIEDUNSPECIFIED
Date : 10 April 2006
Identification Number : 10.1088/1126-6708/2006/01/035
Uncontrolled Keywords : hep-th, hep-th
Related URLs :
Additional Information : © 2006. Published with a Creative Commons 4.0 Licence. The published version can be found here: http://dx.doi.org/10.1088/1126-6708/2006/01/035
Depositing User : Symplectic Elements
Date Deposited : 22 Dec 2015 12:42
Last Modified : 22 Jan 2016 11:43
URI: http://epubs.surrey.ac.uk/id/eprint/809367

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