Multicriticality, Scaling Operators and mKdV Flows for the Symmetric Unitary One Matrix Models
نویسندگان
چکیده
We present a review of the Symmetric Unitary One Matrix Models. In particular we compute the scaling operators in the double scaling limit and the corresponding mKdV ows. We brieey discuss the computation of the space of solutions to the string equation as a subspace of Gr (0)
منابع مشابه
Unitary One Matrix Models: String Equation and Flows
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 τ -function formalism for the flows and we describe its connection to the (big cell of the) Sato Grassmannian Gr via the Plucker embedding of Gr into a fermionic Fock space. Then the space of solutions to the stri...
متن کاملScaling and Fractal Concepts in Saturated Hydraulic Conductivity: Comparison of Some Models
Measurement of soil saturated hydraulic conductivity, Ks, is normally affected by flow patterns such as macro pore; however, most current techniques do not differentiate flow types, causing major problems in describing water and chemical flows within the soil matrix. This study compares eight models for scaling Ks and predicted matrix and macro pore Ks, using a database composed of 50 datasets...
متن کاملMultimatrix Models and the KP-Hierarchy
We analyze the critical points of multimatrix models. In particular we find the critical points of highest multicriticality of the symmetric two-matrix model with an even potential. We solve the model on the sphere and show that these critical points correspond to the (p, q) minimal models with p + q =odd. Based on this experience we give a formulation of minimal models coupled to quantum gravi...
متن کاملLoop Equations and the Topological Phase of Multi - Cut Matrix Models
We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of 2× 2 matrices. We derive from it loop equations which can be expressed as Virasoro constraints on the partition function. We discover a “pure to...
متن کاملQuaternionic Soliton Equations from Hamiltonian Curve Flows in Hp
A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from geometric non-stretching flows of curves in the quaternionic projective space HPn. The derivation adapts the method and results in recent work by one of us on the Hamiltonian structure of non-stretching curve flows in Riemannian symmetric spaces M = G/H by viewing HPn ≃ U(n + 1, H)/U(1, H)× U(n, H) ≃ Sp(n + 1)/Sp(1)× Sp(...
متن کامل