IAS CMP/QFT Group Meeting

Abstract: An intrinsic quantity characterizing a scale-invariant quantum field theory (SFT) is its thermal mass gap, controlling its correlation length at finite temperature. By scale-invariance, this is a pure number in units of the temperature. Using a certain positivity assumption that I will motivate, combined with modular invariance, the torus Casimir energy of 2+1d SFTs defines a structure similar to the “EFT-Hedron”. I will show that the thermal mass gap is encoded in the resulting geometry, and that it is bounded from above, independent of any other theory-dependent data. As a by-product, I will obtain bounds on the shape-dependence of the torus Casimir energy and will study a seemingly new solution saturating the bounds.