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BMS field theory and holography in asymptotically flat space-times

Claudio Dappiaggi

TL;DR

This work advances a holographic perspective for asymptotically flat spacetimes by constructing a free BMS field theory on future/past null infinity and analyzing its quantum structure. It develops the BMS-Klein-Gordon framework, derives a boundary path integral with constraints, and obtains a boundary two-point function governed by a differential equation that encodes evolution along pure supertranslations. A null surface formulation is proposed to connect boundary data with bulk geometry, suggesting that cut functions Z(x^a,z,ar z) can, at least in Minkowski space, reproduce the bulk propagator and potentially enable bulk reconstruction in more general backgrounds. The study highlights the nontrivial IR structure associated with BMS supertranslations and points toward a holographic program for flat spacetimes, including future work on interactions and curved geometries.

Abstract

We explore the holographic principle in the context of asymptotically flat space-times by means of the asymptotic symmetry group of this class of space-times, the so called Bondi-Metzner-Sachs (BMS) group. In particular we construct a (free) field theory living at future (or past) null infinity invariant under the action of the BMS group. Eventually we analyse the quantum aspects of this theory and we explore how to relate the correlation functions in the boundary and in the bulk.

BMS field theory and holography in asymptotically flat space-times

TL;DR

This work advances a holographic perspective for asymptotically flat spacetimes by constructing a free BMS field theory on future/past null infinity and analyzing its quantum structure. It develops the BMS-Klein-Gordon framework, derives a boundary path integral with constraints, and obtains a boundary two-point function governed by a differential equation that encodes evolution along pure supertranslations. A null surface formulation is proposed to connect boundary data with bulk geometry, suggesting that cut functions Z(x^a,z,ar z) can, at least in Minkowski space, reproduce the bulk propagator and potentially enable bulk reconstruction in more general backgrounds. The study highlights the nontrivial IR structure associated with BMS supertranslations and points toward a holographic program for flat spacetimes, including future work on interactions and curved geometries.

Abstract

We explore the holographic principle in the context of asymptotically flat space-times by means of the asymptotic symmetry group of this class of space-times, the so called Bondi-Metzner-Sachs (BMS) group. In particular we construct a (free) field theory living at future (or past) null infinity invariant under the action of the BMS group. Eventually we analyse the quantum aspects of this theory and we explore how to relate the correlation functions in the boundary and in the bulk.

Paper Structure

This paper contains 9 sections, 2 theorems, 118 equations.

Table of Contents

  1. Introduction
  2. BMS fields
  3. From momentum frame to the coordinate frame: an infinite dimensional calculus
  4. The BMS Lagrangian
  5. Path-integral and BMS correlators
  6. From boundary to bulk: a proposal
  7. Conclusions
  8. Elements of white noise as an infinite dimensional calculus
  9. Null surface formulation of general relativity

Key Result

Theorem 1

The support condition $[p(\theta,\varphi)-\pi(p)]\phi(p)=0$ is equivalent to where $\phi$ is a non vanishing function in $\mathcal{C}$ and where $Q_{p-\pi(p)}$ is the multiplication operator in $L^2(N)$ along the elementFrom now on the dependence on the $S^2$ angular variable is implicit unless stated.$p-\pi(p)$ in $N=L^2(S^2)$. At the same time, if we introduce the basis in

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2