BMS Field Theories with $\mathfrak{u}(1)$ Symmetry

TL;DR

This paper explores 2d quantum field theories with BMS and $(1)$ symmetry, analyzing their modular properties, state density, and entropy, and connects these findings to charged flat space cosmologies via holography.

Contribution

It introduces the construction of characters and partition functions for BMS+$(1)$ symmetric theories and derives new asymptotic structure constants with phase shifts, extending previous BMS results.

Findings

Derived the partition function and density of states for BMS+$(1)$ theories.

Calculated the entropy and structure constants showing phase shifts.

Confirmed field theory results with bulk scalar probe computations in charged FSC backgrounds.

Abstract

We investigate quantum field theories in two dimensions (2d) with an underlying Bondi-van der Burgh-Metzner-Sachs (BMS) symmetry augmented by $\mathfrak{u}(1)$ currents. These field theories are expected to holographically capture features of charged versions of cosmological solutions in asymptotically flat 3d spacetimes called Flat Space Cosmologies (FSCs). We conduct a study of the modular properties of these field theories. The characters for the highest weight representations of the symmetry algebra are constructed, and the partition function of the theory is obtained from them. We derive the density of (primary) states and find the entropy and asymptotic values of the structure constants exploiting the modular properties of the partition function and the torus one-point function. The expression for the asymptotic structure constants shows shifts in the weights and one of the central terms and an extra phase compared to the earlier results in the literature for BMS invariant theories without $\mathfrak{u}(1)$ currents present. We reproduce our field results for the structure constants by a bulk computation involving a scalar probe in the background of a charged FSC.