String integrability of defect CFT and dynamical reflection matrices

TL;DR

This paper explores the integrability of a defect conformal field theory (CFT) via string theory, constructing a dynamical reflection matrix that depends on spectral parameters and string coordinates, advancing understanding of holographic duality.

Contribution

It introduces a dynamical reflection matrix in the string theory description of defect CFTs, demonstrating integrability through the construction of a conserved double row transfer matrix.

Findings

Constructed a conserved double row transfer matrix.

Identified a dynamical reflection matrix depending on spectral and embedding coordinates.

Provided evidence for integrability on the string theory side of the duality.

Abstract

The D3-D5 probe-brane system is holographically dual to a defect CFT which is known to be integrable. The evidence comes mainly from the study of correlation functions at weak coupling. In the present work we shed light on the emergence of integrability on the string theory side. We do so by constructing the double row transfer matrix which is conserved when the appropriate boundary conditions are imposed. The corresponding reflection matrix turns out to be dynamical and depends both on the spectral parameter and the string embedding coordinates.