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기하학 수리물리 연구단
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Cut-and-join description of generalized Brezin-Gross-Witten model

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Title
Cut-and-join description of generalized Brezin-Gross-Witten model
Author(s)
Alexandrov A.
Publication Date
2018
Journal
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, v.22, no.6, pp.1347 - 1399
Publisher
INT PRESS BOSTON
Abstract
We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we derive the Virasoro constraints, which completely specify the partition function. We solve them in terms of the cut-and-join operator. The Virasoro constraints lead to the loop equations, which we solve in terms of the correlation functions. Explicit expressions for the coefficients of the tau-function and the free energy are derived, and a compact formula for the genus zero contribution is conjectured. A family of polynomial solutions of the KdV hierarchy, given by the Schur functions, is obtained for the half-integer values of the parameter. The quantum spectral curve and its classical limit are discussed. © by International Press of Boston, Inc.
URI
https://pr.ibs.re.kr/handle/8788114/5930
ISSN
1095-0761
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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