# Asymptotic symmetry **Asymptotic symmetries**, or large gauge transformations, are symmetries of the theory, but not of the solutions. Bulk gauge transformations, on the other hand, are redundancies of the theory. We can define asymptotic symmetry as follows:$\text{Asymptotic symmetry} =\frac{\text{Gauge transformations preserving the BC}}{\text{Trivial gauge transformations}}$where *trivial* means vanishing at boundary. Alternatively, we can work in a gauge-fixed language, in which case asymptotic symmetries are residual gauge transformations that preserve the boundary conditions. To understand how it is related to the definition above, think of gauge fixing as removing trivial gauge, which is like taking the quotient. In [[0001 AdS-CFT|AdS/CFT]], asymptotic symmetries of the bulk become global symmetries of the boundary. For example, with Dirichlet boundary condition fixed to that of a sphere, the asymptotic symmetry group is always the [[0028 Conformal symmetry|conformal]] group, $SO(d,2)$, [[0085 Asymptotic symmetry of AdS3|except in AdS3]] where it becomes the infinite-dimensional group that matches the symmetry of the 2D CFT. This is the most commonly used boundary condition, but in general other boundary conditions can be used. ## Refs - reviews/learning materials - [[Rsc0005 CompereFiorucci Ch1 Surface charges]] - [Strominger talk at String2020](https://www.youtube.com/watch?v=IEsSylfHnKM) - [[Safari2011Thesis]][](https://arxiv.org/pdf/2011.02318.pdf): some good intro to the maths - [[2020#Fiorucci, Ruzziconi]] - Yang-Mills - [[2013#Strominger (Aug)]] - QED - [[2014#He, Mitra, Porfyriadis, Strominger]] - gravity - [[2014#Kapec, Lysov, Pasterski, Strominger]] - general framework - [[2021#Chandrasekaran, Flanagan, Shehzad, Speranza]] - 3+1 - [[2024#Adami, Sheikh-Jabbari, Taghiloo]]: charges and Schwarzian action on the sphere ## Extensions - [[2020#Geiller, Goeller]] - [[2022#Horn]]: asymptotic symmetries that do not preserve the falloff conditions - higher dimensions - [[ChowdhuryMishraPrabhu2022]][](https://arxiv.org/pdf/2201.07813.pdf): non-linearity unavoidable - higher derivative - [[GodazgarLong2022]][](https://arxiv.org/pdf/2201.07014.pdf): [[0425 Gauss-Bonnet gravity|GB]] and Pontryagin - [[0561 Near-horizon symmetry]] ## Alternative methods - [[GodazgarGodazgarPerry2020]]: proposing that all possible action ambiguities should be considered - [[BarnichRuzziconi2021]][](https://arxiv.org/pdf/2103.11253.pdf): celestial Riemann sphere - tidal energy method - [[Fernandez-AlvarezSenovilla2021a]] - [[Fernandez-AlvarezSenovilla2021b]] - log terms and non-smoothness of null infinity - [[Kehrberger2021]][](https://arxiv.org/pdf/2105.08084.pdf) - relaxing determinant condition [[BrockiKowalski-Glikman2021]][](https://arxiv.org/abs/2109.06642) - building block method [](https://arxiv.org/pdf/2012.14050.pdf) ## Examples - [[0085 Asymptotic symmetry of AdS3]] - null surface (2d and 3d) - [[2020#Adami, Sheikh-Jabbari, Taghiloo, Yavartanoo, Zwikel]] - [[0531 Rarita-Schwinger fields|Rarita-Schwinger field]] with a magnetic term - [[Tomova2021]][](https://arxiv.org/pdf/2104.14904.pdf) - a first step towards extending [[0174 Dual supertranslations|dual BMS]] charges to supergravity - gauge theories - at order $O(r)$: [[CampigliaPeraza2021]][](https://arxiv.org/pdf/2111.00973.pdf) - [[0332 Supergravity|SUGRA]] - [[2020FotopoulosStiebergerTaylorZhu2020]] - [[2022#Banerjee, Rahnuma, Singh]] ## Quantum algebra - celestial v.s. [[2018#Distler, Flauger, Horn|DFH]] - [[2021#Campiglia, Laddha]] ## Related - [[0063 Symmetry of CCFT]] - [[0085 Asymptotic symmetry of AdS3]] - [[0010 Celestial holography]] - [[0009 Soft theorems]]