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arXiv · 2502.09272

Relating electrodynamics and gravity in two Euclidean dimensions

Thales F. Bittencourt·Rodrigo F. Sobreiro
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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.

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Thales F. Bittencourt, Rodrigo F. Sobreiro. 2025-02-13. Relating electrodynamics and gravity in two Euclidean dimensions. https://arxiv.org/abs/2502.09272

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