Impossible Symmetries and Conformal Gravity

TL;DR

This paper investigates the role of higher-form symmetries and anomalies in relativistic gapless phases, highlighting the concept of impossible symmetries and analyzing conformal gravity through this lens.

Contribution

It introduces the idea of impossible symmetries that cannot be realized in physical systems and applies this framework to conformal gravity, elucidating its symmetry structure and anomalies.

Findings

Certain higher-form symmetries cannot be realized in Lorentzian systems due to anomalies.

Conformal gravity's symmetries can be understood via anomaly analysis.

Clarification of electric-magnetic duality in linear conformal gravity.

Abstract

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We consider many examples of the general construction. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity.