TY - JOUR

T1 - Reduced unitary matrix models and the hierarchy of τ-functions

AU - Bowick, Mark J.

AU - Morozov, Aleksey

AU - Shevitz, Daniel

N1 - Funding Information:
A.M. acknowledges the hospitality of the High Energy Theory Group at Syracuse University where this research was carried out. He is also indebted to A. Gerasimov, Yu. Makeenko, A. Marshakov, A. Mironov and A. Orlov for illuminating discussions of matrix models and specific details of the unitary case . We thank Greg Moore for pointing out an error in the normalization of t in a preliminary version of this paper. This research was supported by the Outstanding Junior Investigator grant DOE-DE-FG02-85ER40231 and funds from the Office of Sponsored Research of Syracuse University .

PY - 1991/5/6

Y1 - 1991/5/6

N2 - We study reductions of unitary one-matrix models. The unitary model admits an especially rich class of reductions of which the widely known symmetric model is only one. The partition function of a certain class of reduced models is shown to be a product of distinct Toda chain τ-functions. Virasoro constraints are also derived for the case of unitary models. It is claimed, in analogy with the reduced hermitian model, that in the continuous limit the Virasoro constraints must be imposed on a fractional power of the original partition function.

AB - We study reductions of unitary one-matrix models. The unitary model admits an especially rich class of reductions of which the widely known symmetric model is only one. The partition function of a certain class of reduced models is shown to be a product of distinct Toda chain τ-functions. Virasoro constraints are also derived for the case of unitary models. It is claimed, in analogy with the reduced hermitian model, that in the continuous limit the Virasoro constraints must be imposed on a fractional power of the original partition function.

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U2 - 10.1016/0550-3213(91)90365-5

DO - 10.1016/0550-3213(91)90365-5

M3 - Article

AN - SCOPUS:0001640255

SN - 0550-3213

VL - 354

SP - 496

EP - 530

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2-3

ER -