HEP Theory Journal Club

Casimir Energies in 2+1 QFTs

Sebastian Fischetti

McGill

For a change from my usual fare, I'll talk about some ongoing work on (2+1)-dimensional membranes supporting relativistic QFT degrees of freedom. The typical buzzword example is graphene, in which charge carriers rearrange themselves into massless Dirac fermions, but there are more exotic examples like braneworld models. Interpreting the free energy of such systems as a functional of the geometry of the membrane, I'll show in various contexts that this free energy is always locally maximized by a symmetric space (e.g. the round sphere or flat space). This result holds for theories ranging from holographic CFTs with gravitational duals to the free nonminimally coupled massive scalar and the Dirac fermion. If the equilibrium configuration of the membrane is governed by this free energy, this implies that symmetric spaces like the round sphere are disfavored by this QFT contribution to the free energy; their stability is then determined by the competition between this QFT effect and the classical Landau free energy of the membrane. I'll briefly discuss this competition.