Three-point Functions in Aharony--Bergman--Jafferis--Maldacena Theory and Integrable Boundary States

TL;DR

This paper explores three-point correlators in ABJM theory using integrable boundary states, revealing conditions under which the boundary state remains integrable and computing overlaps in these cases.

Contribution

It introduces a novel approach to analyze three-point functions in ABJM theory via integrable boundary states, identifying specific conditions for integrability.

Findings

Boundary state integrability depends on Wick contraction count.

Overlap computations are performed for integrable boundary states.

Integrability is preserved only when Wick contractions are 0 or 1.

Abstract

We investigate the correlators of three single-trace operators in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory from the perspective of integrable boundary states. Specifically, we focus on scenarios where two operators being $1/3$-BPS and the entire correlation function is considered within the twisted-translated frame. The correlator can be expressed as the overlap between a boundary state and a Bethe state. It is found that the boundary state formed by the two $1/3$-BPS operators is integrable only when the number of Wick contractions between the non-BPS operator and one of the $1/3$-BPS operators is 0 or 1. We compute the overlaps for the integrable cases utilizing the symmetries preserved by the correlators.