A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta

Authors: Souvik Banerjee, Kyriakos Papadodimas, Suvrat Raju, Prashant Samantray, Pushkal Shrivastava Preprint number: UUITP-7/19 We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of this correlator is bounded by exp(-βR) where R is the radius of the smallest sphere that contains the polygon formed by the momenta. We argue that, generically, perturbative quantum field theories can saturate this bound through suitably high-order loop diagrams. We also consider holographic theories in d-spacetime dimensions where we show that the leading two-point function of generalized free-fields in such theories saturates the bound in d = 2 and is below the bound for d > 2. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.