Wrapping corrections for non-diagonal boundaries in AdS/CFT

TL;DR

This paper computes wrapping corrections for open strings with non-diagonal boundary conditions in AdS/CFT, interpolating between known diagonal cases, and provides explicit energy calculations at weak coupling.

Contribution

It introduces a method to calculate wrapping corrections for non-diagonal boundary S-matrices in AdS/CFT, extending previous diagonal boundary results.

Findings

Derived one-particle energy corrections at weak coupling up to 6 loops.

Confirmed that results match known diagonal boundary cases when theta=0 or pi/2.

Demonstrated the interpolation between different boundary conditions.

Abstract

We consider an open string stretched between a Y=0 brane and a Y_theta=0 brane. The latter brane is rotated with respect to the former by an angle theta, and is described by a non-diagonal boundary S-matrix. This system interpolates smoothly between the Y-Y (theta =0) and the Y-bar Y (theta = pi/2) systems, which are described by diagonal boundary S-matrices. We use integrability to compute the energies of one-particle states at weak coupling up to leading wrapping order (4, 6 loops) as a function of the angle. The results for the diagonal cases exactly match with those obtained previously.