A thermal Froissart-Gribov formula for CFTs (Quantum Spacetime Seminar Series)

The resurgence of the bootstrap program in CFTs in the last decade has mostly focussed on zero temperature correlators. We propose an extension of the so-called analytic bootstrap for thermal correlators. Thermal two-point functions can be OPE expanded into one point functions of operators. For the two point function of scalar operators, we propose a Froissart-Gribov type formula which "inverts" this expansion, i.e. the formula expresses the one-point functions as an integral of the discontinuity of the two-point function along a certain locus. We test our formula in generalized free field theory, the large N Wilson Fisher theory. More ambitiously, combining information learnt from the inversion formula with the KMS condition, we try to bootstrap the one point functions of the phi^2 and stress tensor operators in the 3D Ising model.