Open Spinning Strings and AdS/dCFT Duality

TL;DR

This paper explores open spinning string solutions on an AdS_4 x S^2-brane, analyzing their boundary conditions, integrability, and dual gauge theory spin chains, revealing new insights into AdS/dCFT duality.

Contribution

It constructs explicit elliptic open string solutions and connects them to integrable open spin chains in the dual gauge theory, advancing understanding of AdS/dCFT correspondence with defects.

Findings

Constructed elliptic folded/circular open string solutions.

Established the Hamiltonian of an open integrable spin chain as the anomalous dimension matrix.

Analyzed Bethe equations and the doubling trick in the thermodynamic limit.

Abstract

We consider open spinning string solutions on an AdS_4 x S^2-brane (D5-brane) in the bulk AdS_5 x S^5 background. By taking account of the breaking of SO(6)_R to SO(3)_H x SO(3)_V due to the presence of the AdS-brane, the open rotating string ansatz is discussed. We construct the elliptic folded/circular open string solutions in the SU(2) and the SL(2) sectors, so that they satisfy the appropriate boundary conditions. On the other hand, in the SU(2) sector of the gauge theory, we compute the matrix of anomalous dimension of the defect operator, which turns out to be the Hamiltonian of an open integrable spin chain. Then we consider the coordinate Bethe ansatz with arbitrary number of impurities, and compare the boundary condition of the Bethe wavefunction with that of the corresponding open string solution. We also discuss the Bethe ansatz for the open SL(2) spin chain with several supports from the string theory side. Then, in both SU(2) and SL(2) sectors, we analyze the Bethe equations in the thermodynamic limit and formulate the `doubling trick' on the Riemann surface associated with the gauge theory.