Celebratio Mathematica — Schwarz — Complete Bibliography

Complete Bibliography

Works connected to Mark John Bowick

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K. N. Anagnostopoulos, M. J. Bowick, and A. Schwarz: “The solution space of the unitary matrix model string equation and the Sato Grassmannian,” Commun. Math. Phys. 148 : 3 (1992), pp. 469–485. MR 1181066 Zbl 0753.35073 ArXiv hep-th/9112066 article

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points \( V_1 \) and \( V_2 \) in the big cell \( \mathrm{Gr}^{(0)} \) of the Sato Grassmannian \( \mathrm{Gr} \). This is a consequence of a well-defined continuum limit in which the string equation has the simple form \( [\mathscr{P},\mathscr{Q}_{-}] = 1 \), with \( \mathscr{P} \) and \( \mathscr{Q}_{-} \) \( 2{\times} 2 \) matrices of differential operators. These conditions on \( V_1 \) and \( V_2 \) yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints \( L_n \) (\( n\geq 0 \)), where \( L_n \) annihilate the two modified-KdV \( \tau \)-functions whose product gives the partition function of the Unitary Matrix Model.

Konstantinos N. Anagnostopoulos	Related
Mark John Bowick	Related