Adjoint Fermion Matrix Models

Abstract

We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an arbitrary interaction potential and turns out to be equivalent to the one for the Hermitean one-matrix model with a logarithmic potential and, therefore, belongs to the same universality class. The explicit solutions for the fermionic two-matrix and $D$-dimensional matrix models are obtained at large $N$ (or in the spherical approximation) for the quadratic potential.

20pp., Latex (4 Latex figures), SMI-93-5

References in corpus (10)

• Induced QCD at Large N
• Combinatorial Solution of the Two-Matrix Model
• The Multicritical Kontsevich-Penner Model
• Exact Solution of Induced Lattice Gauge Theory at Large $N$
• From Virasoro Constraints in Kontsevich's Model to $\mathcal{W}$-constraints in 2-matrix Models
• Symmetry Breaking in the Double-Well Hermitian Matrix Models
• The Large-$N$ Limit of the Two-Hermitian-matrix model by the hidden BRST method
• Correlators of the Kazakov-Migdal Model
• Mixed Model of Induced QCD
• Adjoint Fermions Induce QCD

Cited by in corpus (17)

• Fermionic Matrix Models
• A matrix model for a quantum hall droplet with manifest particle-hole symmetry
• Generalized Penner models to all genera
• Solvable Quantum Grassmann Matrices
• Grassmann Matrix Quantum Mechanics
• Strings, Matrix Models, and Meanders
• W-representations of the fermionic matrix and Aristotelian tensor models
• Fermionic Quantum Gravity
• Polynomial solution of quantum Grassmann matrices
• Bosonic color-flavor transformation for the special unitary group
• Critical Behaviour of a Fermionic Random Matrix Model at Large-N
• The Critical Exponents Of The Matrix Valued Gross-Neveu Model
• Noncommutative probability, matrix models, and quantum orbifold geometry
• Loop equations for generalised eigenvalue models
• The Color--Flavor Transformation of induced QCD
• Fermionic Matrix Models and Bosonization
• Matrix Models of 2D Gravity and Induced QCD