Carrollian Partition Functions and the Flat Limit of AdS

TL;DR

This paper develops a Carrollian boundary framework for the S-matrix in Minkowski space, connecting it to AdS/CFT and revealing symmetry and soft theorem structures through partition functions at null infinity.

Contribution

It introduces a Carrollian partition function approach to the S-matrix, linking asymptotic boundary data with AdS/CFT in the flat limit, and clarifies symmetry actions and soft theorems.

Findings

Carrollian partition functions encode the S-matrix at null infinity.

A simple map relates AdS and Carrollian partition functions.

Symmetries and soft theorems are realized within this boundary framework.

Abstract

The formulation of the S-matrix as a path integral with specified asymptotic boundary conditions naturally leads to the realization of a Carrollian partition function defined on the boundary of Minkowski space. This partition function, specified at past and future null infinity in the case of massless particles, generates Carrollian correlation functions that encode the S-matrix. We explore this connection, including the realization of symmetries, soft theorems arising from large gauge transformations, and the correspondence with standard momentum space amplitudes. This framework is also well-suited for embedding the Minkowski space S-matrix into the AdS/CFT duality in the large radius limit. In particular, we identify the AdS and Carrollian partition functions through a simple map between their respective asymptotic data, establishing a direct correspondence between the actions of symmetries on both sides. Our approach thus provides a coherent framework that ties together various topics extensively studied in recent and past literature.