# A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta

## TL;DR

This paper establishes a universal exponential bound on thermal relativistic correlators at large spacelike momenta, showing saturation in certain quantum field theories and holographic models, and explores implications for high-energy behavior.

## Contribution

It derives a universal bound on thermal correlators at large spacelike momenta and analyzes conditions under which this bound is saturated in quantum and holographic theories.

## Key findings

- Correlators are bounded by $e^{-eta R}$, with $R$ related to the momenta polygon.
- Perturbative QFT can saturate the bound via high-order loops.
- In holographic theories, the bound is saturated in 2D and not exceeded in higher dimensions.

## Abstract

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 these correlators is bounded by $e^{-\beta R}$, where $R$ is the radius of the smallest sphere that contains the polygon formed by the momenta. We show that 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 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.