nLab asymptotic symmetry

Idea

Given a gauge theory (and/or gravity) on a spacetime with asymptotic boundary, certain would-be gauge transformations (diffeomorphisms) that act non-trivially on asymptotic “boundary data” may in fact be identified as physically observable global symmetries and hence have, in contrast to actual gauge symmetries, “direct empirical significance” (DES, Teh 2016).

A basic example is (the symmetry generated by) the ADM mass and the BMS group of asymptotic symmetries on asymptotically flat spacetimes.

Up to technical fine-print (cf. Borsboom & Posthuma 2015) a group of asymptotic symmetries is the coset space of all gauge symmetries that respect boundary data, by the subgroup of bulk gauge transformations which act as the identity map on the asymptotic boundary (cf. Strominger 2018 (2.10.1), Borsboom & Posthuma 2015 p 2):

$$AsymptoticSymmetries \;=\; \frac{ BoundaryAdmissibleGaugeSymmetries }{ BulkGaugeSymmetriesTrivialAtBoundary }$$

Hence if the bulk gauge symmetries form a normal subgroup then the asymptotic symmetries form a quotient group characterized by a short exact sequence of the form

$$1 \to BulkGaugeSymmetriesTrivialAtBoundary \longrightarrow BoundaryAdmissibleGaugeSymmetries \longrightarrow AsymptoticSymmetries \to 1 \,.$$

Related entries

• asymptotic boundary

• asymptotic isometry

• soft graviton theorem

References

Early usage of the term “asymptotic symmetry”:

• Rainer K. Sachs: Asymptotic Symmetries in Gravitational Theory, Phys. Rev. 128 (1962) 2851 [doi:10.1103/PhysRev.128.2851]

  (introducing what came to be known as the BMS group)

In D=3 gravity:

• Steve Carlip: Dynamics of Asymptotic Diffeomorphisms in $(2+1)$-Dimensional Gravity, Class. Quant. Grav. 22 (2005) 3055-3060 [arXiv:gr-qc/0501033, doi:10.1088/0264-9381/22/14/014]

General considerations:

• Nicholas Teh: Galileo’s Gauge: Understanding the Empirical Significance of Gauge Symmetry, Philosophy of Science 83 (2016) 93-118 [doi:10.1086/684196]

In relation to soft graviton theorems:

• Andrew Strominger: Asymptotic Symmetries, section 2.10 in: Lectures on the Infrared Structure of Gravity and Gauge Theory, Princeton University Press (2018) [ISBN:9780691179506, arXiv:1703.05448]

In relation to superselection sectors:

• A. P. Balachandran, V. P. Nair, A. Pinzul, A. F. Reyes-Lega, S. Vaidya: Superselection, boundary algebras, and duality in gauge theories, Phys. Rev. D 106 (2022) 025001 [doi:10.1103/PhysRevD.106.025001, arXiv:2112.08631]

For electromagnetism:

• Silvester Borsboom, Hessel Posthuma: Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory [arXiv:2502.16151]

See also:

• Antoine Rignon-Bret, Simone Speziale: General covariance and boundary symmetry algebras [arXiv:2403.00730]

• Níckolas de Aguiar Alves, Andre G. S. Landulfo: The Sky as a Killing Horizon [arXiv:2504.12514]