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  • Open Access

3D stress tensor for gravity in 4D flat spacetime

Arjun Bagchi1,*, Prateksh Dhivakar1,†, and Sudipta Dutta2,‡

  • *Contact author: abagchi@iitk.ac.in
  • †Contact author: prateksh@iitk.ac.in
  • ‡Contact author: sudipta.dutta@ulb.be
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Phys. Rev. D 113, 066013 – Published 20 March, 2026

DOI: https://doi.org/10.1103/fmvk-vrdz

Abstract

Three-dimensional (3D) Carrollian conformal field theories (CFTs) are potential codimension-one holographic duals of 4D asymptotically flat spacetimes that live on the whole of the null boundary. In this paper, we show that the local stress tensor of the 3D Carrollian conformal theory (without any additional sources) constructed in terms of the geometric structure at asymptotic null infinity naturally encodes both the leading and subleading soft graviton theorems. We relate the 3D Carroll stress tensor to the 2D Celestial one and show how the 3D version naturally localizes the nonlocal 2D Celestial stress tensor. We also comment on the relation with stress tensors in relativistic 3D CFTs and connections to the flat limit of AdS/CFT.

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Outline

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Phys. Rev. D 113, 066013– Published 20 March, 2026
  • Received 7 October 2024
  • Accepted 6 February 2026
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