Nonlinear Renormalization Group Equation for Matrix Models

Abstract

An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining the critical coupling constant and the critical exponent is obtained. As concrete examples, one-matrix models with one and two coupling constants are analyzed and the exact values of the critical coupling constant and the associated critical exponent are found.

12 pages, TIT/HEP-228, NUP-A-93-13 ( a few corrections in formulae, the conclusion not changed)

References in corpus (10)

• Renormalization Group Approach to Matrix Models
• Matter fields with c > 1 coupled to 2d gravity
• A Proposal for Strings at D>1
• A naive matrix-model approach to two-dimensional quantum gravity coupled to matter of arbitrary central charge
• Perturbative analysis of an n-Ising model on a random surface
• The D=1 Matrix Model and the Renormalization Group
• Renormalization Group Approach to Matrix Models and Vector Models
• Renormalization Group Approach to Matrix Models in Two-Dimensional Quantum Gravity
• Exact Beta Functions in the Vector Model and Renormalization Group Approach
• Non-analyticity in the large N renormalization group

Cited by in corpus (20)

• Non-Hermitean Random Matrix Theory: method of hermitization
• Non-Gaussian Non-Hermitean Random Matrix Theory: phase transitions and addition formalism
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• A scenario for the c>1 barrier in non-critical bosonic strings
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Renormalization group approach to multiple-arc random matrix models
• Non-Hermitean Random Matrix Theory: Summation of Planar Diagrams, the "Single-Ring" Theorem and the Disk-Annulus Phase Transition
• Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models
• Renormalization group approach to matrix models via noncommutative space
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• Random vector and matrix and vector theories: a renormalization group approach
• A Renormalization Group Approach to A Yang-Mills Two Matrix Model
• Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function
• Random Geometries and Real Space Renormalization Group
• Renormalization Group for Matrix Models with Branching Interactions
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• A Remark on the Renormalization Group Equation for the Penner Model
• On gonihedric loops and quantum gravity
• Proof of the Lagrangean formalism of Hermitean 1-matrix models to all orders
• Comment on "Remark on the renormalization group equation for the Penner model"