Scalar one-point functions and matrix product states of AdS/dCFT

TL;DR

This paper derives explicit formulas for scalar one-point functions in a defect conformal field theory using integrable spin chain techniques, revealing the integrability properties of the associated matrix product states.

Contribution

It provides a closed-form expression for scalar one-point functions in AdS/dCFT and demonstrates the integrability of the matrix product states involved.

Findings

Explicit formulas for scalar one-point functions

Matrix product states are annihilated by parity odd charges

Discussion of analogous states in D3-D7 setup

Abstract

We determine in a closed form all scalar one-point functions of the defect CFT dual to the D3-D5 probe brane system with k units of flux which amounts to calculating the overlap between a Bethe eigenstate of the integrable SO(6) spin chain and a certain matrix product state of bond dimension k. In particular, we show that the matrix product state is annihilated by all the parity odd charges of the spin chain which has recently been suggested as the criterion for such a state to correspond to an integrable initial state. Finally, we discuss the properties of the analogous matrix product state for the SO(5) symmetric D3-D7 probe brane set-up.