# Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton

## TL;DR

This paper extends the integrability of ABJM determinant operators to all loop orders by deriving asymptotic Bethe ansatz equations for open spin chains attached to giant gravitons, revealing new insights into their boundary symmetries.

## Contribution

It provides the all-loop asymptotic Bethe ansatz equations for ABJM open spin chains with giant gravitons, incorporating boundary symmetries and fermionic dualities.

## Key findings

- Derived all-loop asymptotic Bethe ansatz equations.
- Identified the role of boundary symmetries in integrability.
- Resolved discrepancies through gauge transformations.

## Abstract

In our previous work, the two-loop integrability of ABJM determinant like operator has been well established. In this paper, we push the integrability to all loop orders. The asymptotic Bethe ansatz equations for ABJM determinant like operator (open string attached on giant graviton) are obtained. In the derivation, the symmetries preserved by the bulk and the boundary played a crucial role. Taking the weak coupling limit and applying appropriate fermionic dualities, we obtained a different set of scalar sector Bethe equations with our previous results. When the "gauge" transformation on Bethe equations was introduced, the discrepancy disappeared.