One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT

TL;DR

This paper calculates one-point functions of non-protected scalar operators in a defect conformal field theory derived from N=4 SYM, revealing explicit formulas and numerical results for operators with various excitations.

Contribution

It provides the first explicit formulas for one-point functions of Bethe eigenstates in the SO(5) symmetric D3-D7 defect CFT, including dependence on instanton number.

Findings

Closed-form expressions for one-point functions with few excitations.

Validation of formulas for any instanton number.

Numerical results for operators with more excitations.

Abstract

We study tree level one-point functions of non-protected scalar operators in the defect CFT, based on N=4 SYM, which is dual to the SO(5) symmetric D3-D7 probe brane system with non-vanishing instanton number. Whereas symmetries prevent operators from the SU(2) and SU(3) sub-sectors from having non-vanishing one-point functions, more general scalar conformal operators, which in particular constitute Bethe eigenstates of the integrable SO(6) spin chain, are allowed to have non-trivial one-point functions. For a series of operators with a small number of excitations we find closed expressions in terms of Bethe roots for these one-point functions, valid for any value of the instanton number. In addition, we present some numerical results for operators with more excitations.