String Integrability on the Coulomb Branch

TL;DR

This paper demonstrates that the integrability of the AdS string is preserved on the Coulomb branch of N=4 super-Yang-Mills theory by constructing a reflection matrix that encodes conserved charges.

Contribution

It introduces a dynamical, spectral parameter dependent reflection matrix for open strings ending on a D3-brane, showing integrability is maintained.

Findings

Boundary conditions preserve integrability.

Constructed a reflection matrix encoding conserved charges.

Confirmed integrability on the Coulomb branch.

Abstract

The Coulomb branch of the N = 4 super-Yang-Mills theory is described by a D3-brane in the bulk of AdS_5 x S^5. We show that boundary conditions on this D3-brane preserve integrability of the AdS string. For that matter we construct dynamical and spectral parameter dependent reflection matrix that encodes an infinite number of conserved charges on the worldsheet of an open string ending on the D-brane.