Matrix model as a mirror of Chern-Simons theory | Zendy

Mina Aganagic | Zendy; Albrecht Klemm | Zendy; Marcos Mariño | Zendy; Cumrun Vafa | Zendy

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Matrix model as a mirror of Chern-Simons theory

Author(s) -

Mina Aganagic,

Albrecht Klemm,

Marcos Mariño,

Cumrun Vafa

Publication year - 2004

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2004/02/010

Subject(s) - mirror symmetry , superstring theory , chern–simons theory , gauge theory , matrix (chemical analysis) , pure mathematics , mathematics , mathematical physics , theoretical physics , physics , algebra over a field , supersymmetry , materials science , composite material

Using mirror symmetry, we show that Chern-Simons theory on certain manifoldssuch as lens spaces reduces to a novel class of Hermitian matrix models, wherethe measure is that of unitary matrix models. We show that this agrees with themore conventional canonical quantization of Chern-Simons theory. Moreover,large N dualities in this context lead to computation of all genus A-modeltopological amplitudes on toric Calabi-Yau manifolds in terms of matrixintegrals. In the context of type IIA superstring compactifications on theseCalabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2manifolds) this leads to engineering and solving F-terms for N=1 supersymmetricgauge theories with superpotentials involving certain multi-trace operators.Comment: harvmac, 54 pages, 13 figure

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