AdS/dCFT one-point functions of the SU(3) sector

TL;DR

This paper presents a closed-form, determinant-type formula for tree-level one-point functions in the SU(3) sector of a defect CFT, validated through analytical and numerical tests, extending previous SU(2) results.

Contribution

It introduces a novel determinant formula for SU(3) one-point functions at k=2, based on overlap calculations with Bethe eigenstates and matrix product states.

Findings

The formula passes multiple analytical tests.

Numerical checks confirm the formula's validity.

Differences with the SU(2) case are discussed.

Abstract

We propose a closed formula for the tree-level one-point functions of non-protected operators belonging to an SU(3) sub-sector of the defect CFT dual to the D3-D5 probe brane system with background gauge field flux, k, valid for k=2. The formula passes a number of non-trivial analytical and numerical tests. Our proposal is based on expressing the one-point functions as an overlap between a Bethe eigenstate of the SU(3) spin chain and a certain matrix product state, deriving various factorization properties of the Gaudin norm and performing explicit computations for shorter spin chains. As its SU(2) counterpart, the one-point function formula for the SU(3) sub-sector is of determinant type. We discuss the the differences with the SU(2) case and the challenges in extending the present formula beyond k=2.