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Unitary One Matrix Models: String Equation And Flows, Konstantinos N. Anagnostopoulos, Mark Bowick
Unitary One Matrix Models: String Equation And Flows, Konstantinos N. Anagnostopoulos, Mark Bowick
Physics - All Scholarship
We review the Symmetric Unitary One Matrix Models. In particular we discuss the string equation in the operator formalism, the mKdV flows and the Virasoro Constraints. We focus on the -function formalism for the flows and we describe its connection to the (big cell of the) Sato Grassmannian Gr (0) via the Plucker embedding of Gr (0) into a fermionic Fock space. Then the space of solutions to the string equation is an explicitly computable subspace of Gr (0) \Theta Gr (0) which is invariant under the flows.
The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz
The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz
Physics - All Scholarship
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 Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P; Q \Gamma ] = 1, with P and Q \Gamma 2 \Theta 2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations …