Two-Loop Spectroscopy of Short ABJM Operators

TL;DR

This paper analyzes the two-loop spectrum of short operators in planar ABJM theory, developing new methods to solve Bethe ansatz equations and identifying novel eigenvalues and state sequences.

Contribution

It introduces a method for solving OSp(6|4) Bethe equations for short operators and identifies new rational eigenvalues in ABJM theory.

Findings

Identified three new sequences of rational eigenvalues.

Developed a solution method for length-4 operators with many excitations.

Analyzed low-lying states in the OSp(4|2) and SL(2|1) sectors.

Abstract

We study the spectrum of anomalous dimensions of short operators in planar ABJM theory at two loops. Specifically we develop a method for solving the OSp(6|4) Bethe ansatz equations for a certain class of unpaired length-4 states with arbitrarily high number of excitations, and apply it to identify three new sequences of rational eigenvalues. Results for low-lying paired states in the OSp(4|2) sector are obtained by direct diagonalization of the spin chain Hamiltonian. We also study the SL(2|1) sector and identify the set of states that corresponds to the SL(2)-like Bethe ansatz of Gromov and Vieira. Finally we extend part of our analysis to length-6 operators.