Spectral Flow in 3D Flat Spacetimes

TL;DR

The article develops and tests spectral flow symmetry for extended $\mathfrak{bms}_3$ algebras in 3D flat spacetimes, integrating gravity and dual field theory perspectives. It constructs gravity models (Einstein, $\mathcal{N}=4$ flat supergravity, and their reloaded variants) with boundary conditions that realize $\mathfrak{bms}_3$ augmented by two $\hat{\mathfrak{u}}(1)$ currents, and derives their asymptotic symmetries and FSC entropy. In parallel, it defines field-theory partition functions and uses spectral flow automorphisms to obtain a Cardy-like entropy formula, showing precise agreement with the gravity calculations, including logarithmic corrections. The results illuminate how spectral flow invariance constrains thermal properties across dual descriptions and bolster flat space holography as a robust framework for quantum gravity in asymptotically flat spacetimes. The work also opens avenues for exploring richer algebras and higher-spin extensions in flat holography and clarifies how boundary currents and R-symmetries shape entropy in both gravity and field theory sectors.

Abstract

In this paper we investigate spectral flow symmetry in asymptotically flat spacetimes both from a gravity as well as a putative dual quantum field theory perspective. On the gravity side we consider models in Einstein gravity and supergravity as well as their "reloaded" versions, present suitable boundary conditions, determine the respective asymptotic symmetry algebras and the thermal entropy of cosmological solutions in each of these models. On the quantum field theory side we identify the spectral flow symmetry as automorphisms of the underlying symmetry algebra of the theory. Using spectral flow invariance we then determine the thermal entropy of these quantum field theories and find perfect agreement with the results from the gravity side. In addition we determine logarithmic corrections to the thermal entropy.