Thermal correlator at null infinity

TL;DR

This paper develops a formalism for calculating thermal Carrollian correlators at null infinity, deriving Feynman rules, propagators, and analyzing their properties in position and momentum space, including finite temperature effects.

Contribution

It introduces a novel approach to compute thermal correlators in Carrollian theories, including explicit propagator forms and finite temperature four-point functions.

Findings

Propagators are quadrupled due to field doubling.

Position space correlators are independent of contour choice.

Finite temperature four-point correlators reduce to zero temperature limits.

Abstract

We study the thermal Carrollian correlators at null infinity in the real-time formalism. We derive the Feynman rules to calculate these correlators in the position space. We compute the bulk-to-bulk, bulk-to-boundary and boundary-to-boundary propagators for massless scalar theory. Due to the doubling of the fields degrees of freedom, the number of each propagator is quadrupled. The bulk-to-boundary propagators have the form of (extended) Bose-Einstein distribution in the position space. Utilizing the contour integral of the propagators, we can transform the Feynman rules to momentum space. Interestingly, while the external lines and amplitudes in momentum space depend on the contour, Carrollian correlators in position space are independent of it. We show how to compute four-point correlators at finite temperature. The tree level correlators can be written as the summation of Barnes zeta functions and reduce to the ones in the zero temperature limit.