asymptotic symmetries
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Author(s):  
David Nicolas Prinz ◽  
Alexander Schmeding

Abstract We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi--Metzner--Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Finally, we verify the Trotter property as well as the commutator property. As an outlook, we comment on the situation of related asymptotic symmetry groups. In particular, the much more involved situation of the Newman--Unti group is highlighted, which will be studied in future work.


2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Nabamita Banerjee ◽  
Tabasum Rahnuma ◽  
Ranveer Kumar Singh

Abstract Asymptotic symmetry plays an important role in determining physical observables of a theory. Recently, in the context of four dimensional asymptotically flat pure gravity and $$ \mathcal{N} $$ N = 1 supergravity, it has been proposed that OPEs of appropriate celestial amplitudes can be used to find their asymptotic symmetries. In this paper we find the asymptotic symmetry algebras of four dimensional Einstein-Yang-Mills and Einstein-Maxwell theories using this alternative approach, namely using the OPEs of their respective celestial amplitudes. The algebra obtained here are in agreement with the known results in the literature.


2022 ◽  
Vol 4 (5) ◽  
pp. 1-52
Author(s):  
Giuseppe Gaeta ◽  
◽  
Roma Kozlov ◽  
Francesco Spadaro ◽  
◽  
...  

<abstract><p>We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.</p></abstract>


Author(s):  
Bilyana Lyudmilova Tomova

Abstract In this paper we study the magnetic charges of the free massless Rarita-Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang-Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Yorgo Pano ◽  
Sabrina Pasterski ◽  
Andrea Puhm

Abstract Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the soft charges associated to the fermionic layers that tie this structure together. This extends the analysis of conformally soft currents for photons and gravitons which have been shown to generate asymptotic symmetries in gauge theory and gravity to infinite-dimensional fermionic symmetries. We construct fermionic charge operators in 2D celestial CFT from a suitable inner product between 4D bulk field operators and spin s = $$ \frac{1}{2} $$ 1 2 and $$ \frac{3}{2} $$ 3 2 conformal primary wavefunctions with definite SL(2, ℂ) conformal dimension ∆ and spin J where |J| ≤ s. The generator for large supersymmetry transformations is identified as the conformally soft gravitino primary operator with ∆ = $$ \frac{1}{2} $$ 1 2 and its shadow with ∆ = $$ \frac{3}{2} $$ 3 2 which form the left and right corners of the celestial gravitino diamond. We continue this analysis to the subleading soft gravitino and soft photino which are captured by degenerate celestial diamonds. Despite the absence of a gauge symmetry in these cases, they give rise to conformally soft factorization theorems in celestial amplitudes and complete the celestial pyramid.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Miguel Campiglia ◽  
Javier Peraza

Abstract Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which O(1) and O(r) charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Alfredo Pérez

Abstract Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from “magnetic” and “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For the electric contraction, because the lapse function does not appear in the boundary term needed to ensure a well-defined action principle, the asymptotic symmetry algebra is truncated, for Regge-Teitelboim parity conditions, to the semidirect sum of spatial rotations and spatial translations. Similarly, with Henneaux-Troessaert parity conditions, the asymptotic symmetries are given by the semidirect sum of spatial rotations and an infinite number of parity odd supertranslations. Thus, from the point of view of the asymptotic symmetries, the magnetic contraction can be seen as a smooth limit of General Relativity, in contrast to its electric counterpart.


2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Sabrina Pasterski

AbstractLecture notes prepared for the 2021 SAGEX PhD School in Amplitudes hosted by the University of Copenhagen August 10th through 13th. Topics covered include: the manifestation of asymptotic symmetries via soft theorems, their organization into currents in a celestial CFT, aspects of the holographic dictionary, a literature guide, and accompanying exercises.


2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hadi Godazgar ◽  
Mahdi Godazgar ◽  
Ricardo Monteiro ◽  
David Peinador Veiga ◽  
C. N. Pope

Abstract A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Liénard-Wiechert potential to a large gauge transformation.


2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Sabrina Pasterski ◽  
Andrea Puhm ◽  
Emilio Trevisani

Abstract We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} $$ 0 1 2 1 3 2 2 we classify and construct all SL(2,ℂ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,ℂ) conformal dimension ∆ and spin J. Radiative conformal primary wavefunctions have J = ±s and give rise to conformally soft theorems for special values of ∆ ∈ $$ \frac{1}{2}\mathbb{Z} $$ 1 2 ℤ . They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have |J| ≤ s. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.


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