BMS Field Theories and Weyl Anomaly

TL;DR

This work derives the Weyl (trace) anomaly for two-dimensional BMS-invariant (Carrollian) field theories living on null surfaces, showing the anomaly is controlled by the central charge $c_M$ and takes the form $\langle T^{\alpha}{}_{\alpha} \rangle_e = \frac{4\pi}{3} c_M \partial^2_{\sigma} \Omega$. By establishing Carrollian delta-function identities and Ward identities on both null plane and null cylinder backgrounds, the authors compute BMS stress-tensor OPEs and correlators, enabling a quantum-breaking of Weyl invariance in these non-Lorentzian theories. The nontrivial response of the partition function to Weyl transformations is captured by a Carrollian Liouville action, $S_{\text{cL}} = \frac{8\pi}{3} c_M \int d^2\sigma \, \partial_{\sigma} \Omega \partial_{\sigma} \Omega$, highlighting a distinct structure from relativistic Liouville theory. These results illuminate aspects of flat-space holography, tensionless-string limits, and the broader landscape of nonrelativistic/Carrollian anomalies, and point to future work including the $c_L\neq0$ case and holographic checks in 3d flat spacetimes.

Abstract

Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.