1991/12/21 by Konstantinos N. Anagnostopoulos, Mark J. Bowick, Albert Schwarz
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.1007/bf02096545
published as Commun.Math.Phys. 148 (1992) 469-486 · 21 pages
arxiv created 1991/12/21 · openalex publication_date 1992/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 V1 and V2 in the big cell \Gr of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form \lb \cp ,\cq- \rb =\hbox\rm 1, with \cp and \cq- 2× 2 matrices of differential operators. These conditions on V1 and V2 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 Łn (n≥ 0), where Łn annihilate the two modified-KdV \t-functions whose product gives the partition function of the Unitary Matrix Model.