One-point Functions in Defect CFT and Integrability

TL;DR

This paper computes one-point functions in a defect conformal field theory using integrability techniques, expressing results as overlaps of Bethe eigenstates with matrix product states, including determinant formulas and relations to known states.

Contribution

It introduces a novel method to calculate one-point functions in defect CFTs via overlaps with matrix product states, providing explicit formulas and relations to known quantum states.

Findings

Determinant formulas for k=2 case

Relation between half-filling state and Néel state

Results for the infinite k limit

Abstract

We calculate planar tree level one-point functions of non-protected operators in the defect conformal field theory dual to the D3-D5 brane system with k units of the world volume flux. Working in the operator basis of Bethe eigenstates of the Heisenberg XXX_{1/2} spin chain we express the one-point functions as overlaps of these eigenstates with a matrix product state. For k=2 we obtain a closed expression of determinant form for any number of excitations, and in the case of half-filling we find a relation with the N\'eel state. In addition, we present a number of results for the limiting case of infinite k.