## Symmetries and topological operators, on average

Andrea Antinucci, Giovanni Galati, Giovanni Rizi, Marco Serone

SciPost Phys. 15, 125 (2023) · published 29 September 2023

- doi: 10.21468/SciPostPhys.15.3.125
- Submissions/Reports

### Abstract

We study Ward identities and selection rules for local correlators in disordered theories where a 0-form global symmetry of a QFT is explicitly broken by a random coupling $h$ but it re-emerges after quenched average. We consider $h$ space-dependent or constant. In both cases we construct the symmetry operator implementing the group action, topological after average. In the first case, relevant in statistical systems with random impurities, such symmetries can be coupled to external backgrounds and can be gauged, like ordinary symmetries in QFTs. We also determine exotic selection rules arising when symmetries emerge after average in the IR, explaining the origin of LogCFTs from symmetry considerations. In the second case, relevant in AdS/CFT to describe the dual boundary theory of certain bulk gravitational theories, the charge operator is not purely codimension-1, it can be defined only on homologically trivial cycles and on connected spaces. Selection rules for average correlators exist, yet such symmetries cannot be coupled to background gauge fields in ordinary ways and cannot be gauged. When the space is disconnected, in each connected component charge violation occurs, as expected from Euclidean wormholes in the bulk theory. Our findings show the obstruction to interpret symmetries emergent after average as gauged in the bulk.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Andrea Antinucci, -
^{1}^{2}Giovanni Galati, -
^{1}^{2}Giovanni Rizi, -
^{1}^{2}Marco Serone

^{1}Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]^{2}INFN Sezione di Trieste / INFN Trieste

- European Research Council [ERC]
- Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])