BGWM as Second Constituent of Complex Matrix Model

Details BGWM as Second Constituent of Complex Matrix Model BGWM as Second Constituent of Complex Matrix Model

2009-06-17

arxiv.org/abs/0906.3305v2

JHEP 0912:053,2009

Physics

High Energy Physics

High Energy Physics - Theory

42 pages

Scientific paper

10.1088/1126-6708/2009/12/053

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).

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