Heavy Operators in Superconformal Chern-Simons Theory

TL;DR

This paper analyzes scalar operator anomalous dimensions in ABJM theory's SU(2) sector at large N, revealing non-planar effects, a diagonalizable mixing matrix, and implications for dual gravity and integrability.

Contribution

It introduces a double coset ansatz to diagonalize the two-loop mixing matrix for large N scalar operators, incorporating non-planar contributions.

Findings

Diagonalization of the mixing matrix using a double coset ansatz.

Anomalous dimension spectrum depends on giant graviton size.

Subleading corrections suggest potential loss of integrability.

Abstract

We study the anomalous dimensions for scalar operators in ABJM theory in the SU(2) sector. The operators we consider have a classical dimension that grows as N in the large N limit. Consequently, the large N limit is not captured by summing planar diagrams - non-planar contributions have to be included. We find that the mixing matrix at two-loop order is diagonalized using a double coset ansatz, reducing it to the Hamiltonian of a set of decoupled oscillators. The spectrum of anomalous dimensions, when interpreted in the dual gravity theory, shows that the energy of the fluctuations of the corresponding giant graviton is dependent on the size of the giant. The first subleading corrections to the large N limit are also considered. These subleading corrections to the dilatation operator do not commute with the leading terms, indicating that integrability may not survive beyond the large N limit.