Matrix Model as a Mirror of Chern-Simons Theory

Details Matrix Model as a Mirror of Chern-Simons Theory Matrix Model as a Mirror of Chern-Simons Theory

2002-11-11

arxiv.org/abs/hep-th/0211098v1

JHEP 0402 (2004) 010

Physics

High Energy Physics

High Energy Physics - Theory

harvmac, 54 pages, 13 figures

Scientific paper

10.1088/1126-6708/2004/02/010

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators.

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