The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus

TL;DR

This work advances the field-theory description of BPS monopole operators in ABJM by performing a semiclassical quantization on $S^2$ to map the chiral ring and moduli space, revealing a $\mathbb{Z}_k$-cover structure of $Sym^N(\mathbb{C}^4/\mathbb{Z}_k)$ for the equal-rank case and clarifying $k$-ality sectors. It connects field-theory operators to giant-torus configurations in AdS$^4$/CFT$^3$, by constructing ABJM duals to fuzzy-sphere giants and analyzing fluctuations around monopole backgrounds that reproduce the energy and angular-momentum relations expected from gravity. The paper also discusses broader BPS sectors, showing how flux quantization and nonperturbative monopoles enlarge the chiral ring and hint at black-hole microstate counting, while identifying discrete torsion effects tied to the $\mathbb{Z}_k$ fiber structure. The framework strengthens the ABJM holographic dictionary, clarifies dibaryon/operator structure, and lays groundwork for understanding nontrivial BPS configurations in 3d SCFTs.

Abstract

We study the BPS spectrum of monopole operators in ABJM theory. First we work out the complete spectrum of the chiral ring by using a semiclassical analysis of the field theory compactified on a two sphere. By properly taking into account the full quantization condition of monopole charges, we show that the moduli space of ABJM theory with Chern-Simons level k, -k is a particular Z_k cover of the symmetric product of C^4/Z_k. We also work out in detail the spectrum of fluctuations around half-BPS monopole configurations and we find candidate states for a dual BPS configuration to the giant torus solution found by Nishioka and Takayanagi in the supergravity limit. We also discuss more general BPS states.