To gauge or to double gauge? Matrix models, global symmetry, and black hole cohomologies

A bstract We study the structure of the Hilbert space of gauged matrix models with a global symmetry. In the first part of the paper, we focus on bosonic matrix models with U(2) gauge group and SO( d ) global symmetry, and consider singlets under both the gauge and global symmetry. We show how such “double-gauged” matrix models can be described in terms of a simpler SO(3) single-matrix model. In the second part of the paper, we consider the so-called BMN subsector of the $$ \mathcal{N}=4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> SU( N ) super Yang-Mills theory, which is closely related to the BMN matrix model. Among the 1/16 BPS operators in this sector, “non-graviton” operators were recently discovered, which are expected to relate to the microstates of supersymmetric AdS 5 black holes. We show that a double gauging of this model, where one projects onto SU(3) R R-symmetry singlets, considerably simplifies the analysis of the non-graviton spectrum. In particular, for low values of N , we show that (almost) all graviton operators project out of the spectrum, while important classes of non-graviton operators remain. In the N = 3 case, we obtain a closed form expression for the superconformal index of singlet non-gravitons, which reveals structural features of their spectrum.