HEP Theory Journal Club

More on Vacuum Energies in 2+1 CFTs

Sebastian Fischett

McGill

I'll discuss some updated results on Casimir energies of 2+1 CFTs living on time cross a deformed two-sphere; in appropriate contexts these theories can be thought of as effective descriptions of excitations living on three-dimensional membranes (e.g. graphene). When working perturbatively about the round sphere, this Casimir energy (which is a functional of the geometry of the two-sphere) can be shown to be negative in any CFT: that is, the round sphere is a local maximum of the Casimir energy. For holographic CFTs with Einstein gravity duals, one can in fact show that the round sphere is a global maximum. In this talk I'll focus on quantitative, numerical comparisons between the Casimir energies of holographic CFTs, the conformally-coupled scalar, and the free Dirac fermion living on highly-deformed spheres. The main takeaway is a puzzle: the Casimir energies of the holographic CFT and of the Dirac fermion appear to agree exceptionally closely, far beyond what can be explained by mere conformal invariance. I'd like to pick all of your brains for a potential explanation of this effect.