Nonabelian Berry Phase, Yang-Mills Instanton and USp(2k) Matrix Model

TL;DR

This paper computes the nonabelian Berry phase in a USp(2k) matrix model, revealing instanton-like singularities associated with spacetime points, which are characterized as BPST instantons on a four-dimensional paraboloid.

Contribution

It introduces a method to compute the nonabelian Berry phase in the USp(2k) matrix model and identifies instanton configurations as singularities in the spacetime structure.

Findings

Identification of su(2) Lie algebra valued singularities at spacetime points

Recognition of these singularities as BPST instantons on a paraboloid

Connection between Berry phase and instanton configurations in matrix models

Abstract

The nonabelian Berry phase is computed in the T dualized quantum mechanics obtained from the USp(2k) matrix model. Integrating the fermions, we find that each of the spacetime points X_{\nu}^{(i)} is equipped with a pair of su(2) Lie algebra valued pointlike singularities located at a distance m_{(f)} from the orientifold surface. On a four dimensional paraboloid embedded in the five dimensional Euclidean space, these singularities are recognized as the BPST instantons.