Nonsupersymmetric strong coupling background from the largeNquantum mechanics of two matrices coupled via a Yang-Mills interaction

Abstract

We derive a planar sector of the large N nonsupersymmetric background of the quantum mechanical Hamiltonian of two Hermitian matrices coupled via a Yang-Mills interaction, in terms of the density of eigenvalues of one of the matrices. This background satisfies an implicit nonlinear integral equation, with a perturbative small coupling expansion and a solvable large coupling solution, which is obtained. The energy of system and the expectation value of several correlators are obtained in this strong coupling limit. They are free of infrared divergences. * Joao.rodrigues@wits.ac.za 1 By matrix models we mean integrals over matrices or the quantum mechanics of matrix valued degrees of freedom.2 See also [26] PHYSICAL REVIEW D 82, 085030 (2010) 1550-7998= 2010=82(8)=085030 (8) 085030-1

Free particles from Brauer algebras in complex matrix models

“…In The projector is written in terms of the k-contraction operator C (k) defined by 36) and the projector p α which projects the holomorphic half of V ⊗k ⊗V ⊗k to the representation α. It is proved in Appendix E that the projector takes the form…”

“…where Z denotes complex conjugate of Z. Studies of the same model in terms of two hermitian matrices are done in [35,36].…”