Emergent Symmetries in Ensemble Averages
Abstract
It is widely believed that there are no exact global symmetries in quantum gravity. We review recent works showing that global symmetries can nevertheless emerge after ensemble averages of theories, as encountered in holography. As a precision case study, we discuss the ensemble average of two-dimensional Narain-type conformal field theories associated with an even quadratic form of general signature, which is computed by the Siegel-Weil formula and interpreted as a sum over geometries in a three-dimensional Abelian Chern-Simons theory. Global symmetries of the bulk anyons can emerge after the average, as T-dualities relating different theories in the ensemble are "folded" into symmetries of a single theory (duality origami). We discuss the relation to the Swampland program, including the emergence of global symmetries at infinite distance. Finally, we recast strong-to-weak spontaneous symmetry breaking (SWSSB) of mixed states as an emergence of symmetries in ensemble averages; in holography, wormholes connecting the two sides of a thermofield-double construction provide its bulk realization. This motivates a new Swampland conjecture.
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BibTeX
@misc{yamazaki2026emergent,
title = {{Emergent Symmetries in Ensemble Averages}},
author = {Masahito Yamazaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36542},
eprint = {2609.36542},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36542},
}
RIS
TY - UNPB
TI - Emergent Symmetries in Ensemble Averages
AU - Masahito Yamazaki
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36542
UR - https://arxiv.org/abs/2609.36542
AB - It is widely believed that there are no exact global symmetries in quantum gravity. We review recent works showing that global symmetries can nevertheless emerge after ensemble averages of theories, as encountered in holography. As a precision case study, we discuss the ensemble average of two-dimensional Narain-type conformal field theories associated with an even quadratic form of general signature, which is computed by the Siegel-Weil formula and interpreted as a sum over geometries in a three-dimensional Abelian Chern-Simons theory. Global symmetries of the bulk anyons can emerge after the average, as T-dualities relating different theories in the ensemble are "folded" into symmetries of a single theory (duality origami). We discuss the relation to the Swampland program, including the emergence of global symmetries at infinite distance. Finally, we recast strong-to-weak spontaneous symmetry breaking (SWSSB) of mixed states as an emergence of symmetries in ensemble averages; in holography, wormholes connecting the two sides of a thermofield-double construction provide its bulk realization. This motivates a new Swampland conjecture.
ER -