Symmetry Transmutation and Anomaly Matching

TL;DR

This paper investigates how certain UV symmetries become higher-form symmetries in the IR, demonstrating this transmutation through examples and anomaly matching, and contrasting it with symmetry fractionalization.

Contribution

It introduces the concept of symmetry transmutation, showing how UV symmetries can become exact higher-form symmetries in the IR, with implications for anomaly matching.

Findings

Symmetry transmutation is a widespread phenomenon in various systems.

UV baryon-number symmetry can transmute into a discrete one-form symmetry.

Anomaly matching confirms the equivalence of UV and IR symmetries in this transmutation.

Abstract

We explore a situation where a global symmetry of the ultraviolet (UV) theory does not act faithfully on the local infrared (IR) degrees of freedom, but instead acts effectively as a higher-form symmetry. We refer to this phenomenon as symmetry transmutation, where the UV symmetry is "transmuted" into a higher-form symmetry in the IR. Notably, unlike emergent (accidental) symmetries, which are approximate, these symmetries are exact. We illustrate the ubiquity of this phenomenon in various continuum and lattice systems and provide examples where the 't Hooft anomalies of the UV symmetry are matched by those of the new higher-form symmetry in the IR. We also show that in certain phases and for certain energies, the UV baryon-number symmetry of one-flavor QCD is transmuted into a discrete one-form global symmetry. Finally, we compare our symmetry transmutation to the well-known phenomenon of symmetry fractionalization.