Twisted Sectors in Gravity Duals of N=4 Chern-Simons Theories

TL;DR

This work analyzes gravity duals of ${\cal N}=4$ Chern-Simons theories by examining twisted sectors arising from orbifold singularities in the internal geometry. By constructing the ${\cal N}=2$ vector multiplet action on ${\rm AdS}_4\times{\mathbf S}^3$ and performing a careful Kaluza-Klein decomposition, the authors derive the complete KK spectrum and organize it into 1/2-BPS representations of $OSp(4|4)$. They then compute a superconformal character and an index, demonstrating exact agreement with twisted-sector indices (including monopole operators) calculated on the boundary gauge theory, thereby providing a nontrivial AdS/CFT check and linking monopole operators to wrapped M2-branes. The results illuminate the interplay between discrete torsion, boundary conditions for Betti multiplets, and spectra in orbifold backgrounds, and lay groundwork for extending these methods to more general ${\cal N}=2$ Chern-Simons theories.

Abstract

We study Kaluza-Klein modes of a d=7, N=2 vector multiplet in AdS_4 x S^3. Such modes arise in the context of AdS/CFT as dual objects of a class of gauge invariant operators in N=4 Chern-Simons theories. We confirm that the Kaluza-Klein modes precisely reproduce the BPS spectrum of the operators.