Fermionic matrix models

被引:32
作者
Semenoff, GW [1 ]
Szabo, RJ [1 ]
机构
[1] UNIV OXFORD, DEPT THEORET PHYS, OXFORD OX1 3NP, ENGLAND
来源
INTERNATIONAL JOURNAL OF MODERN PHYSICS A | 1997年 / 12卷 / 12期
关键词
D O I
10.1142/S0217751X97001328
中图分类号
O57 [原子核物理学、高能物理学];
学科分类号
070202 ;
摘要
We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-matrix, two-matrix and gauge-invariant D-dimensional matrix models at large N and compare them with their bosonic counterparts, which are the more familiar Hermitian matrix models. We derive and solve the complete sets of loop equations for the correlators of these models and use these equations to examine critical behavior. The topological large N expansions are also constructed and their relation to other aspects of modern string theory, such as integrable hierarchies, is discussed. We use these connections to discuss the applications of these matrix models to string theory and induced gauge theories. We argue that as such the fermionic matrix models may provide a novel generalization of the discretized random surface representation of quantum gravity in which the genus sum alternates and the sums over genera for correlators have better convergence properties than their Hermitian counterparts. We discuss the use of adjoint fermions instead of adjoint scalars to study induced gauge theories. We also discuss two classes of dimensionally reduced models, a fermionic vector model and a supersymmetric matrix model, and discuss their applications to the branched polymer phase of string theories in target space dimensions D > 1 and also to the meander problem.
引用
收藏
页码:2135 / 2291
页数:157
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