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Chern-Simons Theory, Matrix Models, and Topological Strings$
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Marcos Mariño

Print publication date: 2005

Print ISBN-13: 9780198568490

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568490.001.0001

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STRING THEORY AND GAUGE THEORY

STRING THEORY AND GAUGE THEORY

Chapter:
(p.123) 6 STRING THEORY AND GAUGE THEORY
Source:
Chern-Simons Theory, Matrix Models, and Topological Strings
Author(s):

Marcos Mariño

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568490.003.0006

This chapter examines the relationship between gauge theories and topological strings. A precise correspondence between string theory and gauge theory was formulated by 't Hooft (1974), who used as a starting point the double-line formulation of perturbation theory. The perturbative expansion of a gauge theory with gauge group U(N) can be rewritten in terms of an expansion of double-line Feynman diagrams. This issue has been illustrated in the cases of matrix models and Chern-Simons theory, but it is clear that such a reorganization of the expansion can be made for any U(N) gauge theory, as the double-line representation of the graphs only exploits the underlying gauge symmetry. One important question that needs to be addressed is whether it is possible to make more precise this analogy between U(N) gauge theories and open string theories. Two different topological string theories are considered.

Keywords:   string theory, gauge theory, 't Hooft, topological string theory, Calabi-Yau manifolds, Chern-Simon theory, geometric transitions, open string theory, matrix models

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