Strongly coupled large N spectrum of two matrices coupled via a Yang-Mills interaction

TL;DR

This paper analyzes the large N spectrum of a two-matrix quantum system with Yang-Mills coupling, deriving exact solutions for impurity states and revealing connections to giant magnon bound states.

Contribution

It introduces an exact solution method for the impurity spectrum in a coupled two-matrix model, highlighting the dependence on momenta and the relation to giant magnon states.

Findings

Exact spectrum for two impurities derived

Spectrum depends on two momenta

Connection to giant magnon bound states identified

Abstract

We consider the large N spectrum of the quantum mechanical hamiltonian of two hermitean matrices coupled via a Yang-Mills interaction. In a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity, the difference equation associated with the Yang-Mills interaction is derived and solved exactly for two impurities. In this case, the full string tension corrected spectrum depends on two momenta. For a specific value of one of these momenta, the spectrum has the same structure as that of giant magnon bound states. States with general number of impurities are also discussed.