Relating electrodynamics and gravity in two Euclidean dimensions

TL;DR

This paper establishes a quantum-level equivalence between two-dimensional electrodynamics and gravity by mapping the former onto the latter, revealing unique fermion-gravity couplings that break certain symmetries.

Contribution

It introduces a novel mapping of 2D electrodynamics to gravity including fermions, and analyzes its quantum consistency using path integral and BRST methods.

Findings

Quantum electrodynamics and gravity are equivalent in 2D.

Fermion-gravity coupling violates parity and time-reversal symmetries.

The mapping remains consistent at the quantum level.

Abstract

Two-dimensional electrodynamics coupled to Dirac fermions is mapped onto two-dimensional gravity in the first-order formalism, also including fermions. However, the resulting fermion-gravity coupling deviates from the conventional form, explicitly violating parity and time-reversal symmetries. Additionally, these fermions exhibit an unconventional transformation behavior under $SO(2)$ transformations. Furthermore, we analyze the consistency of this mapping at the quantum level using the path integral formalism and Becchi-Rouet-Stora-Tyutin techniques. Our findings demonstrate that quantum electrodynamics and quantum gravity remain equivalent at the quantum level.