Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence

TL;DR

This paper establishes a correspondence between semiclassical string solutions and long defect operators in AdS/dCFT by deriving a sigma model from both gauge theory and string theory, demonstrating agreement in energies and solutions.

Contribution

It introduces a method to construct coherent states for open spin chains in defect CFTs and derives a sigma model that matches string theory results, extending the AdS/dCFT correspondence.

Findings

Derived a Landau-Lifshitz type sigma model from the open spin chain.

Found complete agreement of energies between string solutions and gauge theory.

Included a pulsating string solution consistent with previous calculations.

Abstract

We consider defect composite operators in a defect superconformal field theory obtained by inserting an AdS_4 x S^2-brane in the AdS_5 x S^5 background. The one-loop dilatation operator for the scalar sector is represented by an integrable open spin chain. We give a description to construct coherent states for the open spin chain. Then, by evaluating the expectation value of the Hamiltonian with the coherent states in a long operator limit, a Landau-Lifshitz type of sigma model action is obtained. This action is also derived from the string action and hence we find a complete agreement in both SYM and string sides. We see that an SO(3)_H pulsating string solution is included in the action and its energy completely agrees with the result calculated in a different method. In addition, we argue that our procedure would be applicable to other AdS-brane cases.