Speaker
Description
Recent advances indicate that 3d gravity may be dual not to a single CFT but to an average over an ensemble of CFTs. We consider a concrete ensemble of CFTs deriving from error-correcting codes via a lattice construction. The very same ensemble also arises from 3d abelian Chern-Simons theory by the gauging of maximal subgroups of the bulk one-form symmetry. Remarkably, the ensemble average over such CFTs agrees with "Chern-Simons gravity," a bulk theory summed over 3d topologies sharing the same boundary, i.e. a Poincaré series akin to that in semiclassical gravity. Here we relate this correspondence to Howe duality, a mathematical framework concerning the representations of two commuting groups. This framework is known to be behind Siegel-Weil formulas underpinning other instances of holography by averaging. Using recent mathematical results from Howe duality for finite fields, we are able to rigorously prove the duality between the code CFT ensemble and Chern-Simons gravity, exhibiting a proof valid at any genus and central charge.
