Monopole operators in N=4 Chern-Simons theories and wrapped M2-branes

TL;DR

This work extends the AdS$_4$/CFT$_3$ monopole-operator program to Abelian ${\cal N}=4$ Chern-Simons quivers by showing that non-diagonal monopole charges form the SU$(p)\times$SU$(q)$ root lattice and correspond to M2-branes wrapped on two-cycles of the internal space ${X_7}$. Using radial quantization, the authors compute BPS-protected charges and construct gauge-invariant monopole operators $\mathfrak{M}_{ab}$ tied to SU$(p)$ and SU$(q)$ root sectors, then map these to M2-branes wrapped on two-cycles with Wilson-line contributions encoding M2 momentum on the Lens space $L_{kq}$. They demonstrate a consistent torsion quantization that forbids fractional M2-branes and relate the spectra to harmonic modes on $L_{kq}$, providing a concrete bulk–boundary dictionary for non-diagonal monopoles. The results pave the way for non-Abelian generalizations, large-$N$ analyses, and investigations of discrete torsion effects on wrapped-brane spectra in AdS$_4$/CFT$_3$ contexts.

Abstract

Monopole operators in Abelian N=4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of untwisted and twisted hypermultiplets, respectively. For monopole operators corresponding to the root vectors, we propose a correspondence between the monopole operators and states of a wrapped M2-brane in the dual geometry.

Figures (2)

• Figure 1: A part of a circular quiver diagram of an ${\cal N}=4$ supersymmetric Chern-Simons theory is shown. Arrows represent chiral multiplets.
• Figure 2: The loci $x_a$ and $y_{\dot a}$ in the base manifold ${\bf S}^5$ are shown. On the loci $x_a$$\mathop{\rm SU}(2)_A\times\mathop{\rm U}(1)_A$ acts as isometry while $\mathop{\rm SU}(2)_B\times\mathop{\rm U}(1)_B$ does as transverse rotations. For $y_{\dot a}$ the roles of these symmetries are exchanged.