Geometric action for extended Bondi-Metzner-Sachs group in four dimensions

Barnich, Glenn; Nguyen, Kévin; Ruzziconi, Romain

doi:10.1007/jhep12(2022)154

Cited by 17 publications

(7 citation statements)

References 71 publications

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“…Higher dimensional exploration: It would be interesting to look into aspects of circuit complexity for d > 2 BMS invariant field theories. Recently, in [108] the geometric action for BMS 4 was given. A natural extension would be to investigate whether any similarity exists for the higher dimensional geometric action and complexity functional.…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

Circuit Complexity for Carrollian Conformal (BMS) Field Theories

Bhattacharyya¹,

Nandi²

2023

Preprint

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We systematically explore the construction of Nielsen's circuit complexity to a non-Lorentzian field theory keeping in mind its connection with flat holography. We consider a 2d boundary field theory dual to 3d asymptotically flat spacetimes with infinite-dimensional BMS 3 as the asymptotic symmetry algebra. We compute the circuit complexity functional in two distinct ways. For the Virasoro group, the complexity functional resembles the geometric action on its co-adjoint orbit. Using the limiting approach on the relativistic results, we show that it is possible to write BMS complexity in terms of the geometric action on BMS co-adjoint orbit. However, the limiting approach fails to capture essential information about the conserved currents generating BMS supertranslations. Hence, we refine our analysis using the intrinsic approach. Here, we use only the symmetry transformations and group product laws of BMS to write the complexity functional. The refined analysis shows a richer structure than only the geometric action. Lastly, we extremize and solve the equations of motion in terms of the group paths and connect our results with available literature.

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Section: Discussion and Future Directionsmentioning

confidence: 99%

Circuit Complexity for Carrollian Conformal (BMS) Field Theories

Bhattacharyya¹,

Nandi²

2023

Preprint

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“…Since also the transformation T(u) depends on the matrix Λ through the conformal factor K Λ (ζ), the work in Ref. [17] proposed the same nomenclature, from parabolic to loxodromic, for the whole group of BMS transformations in Equation (11). By virtue of Equations ( 6), ( 12), ( 14), ( 16) and ( 18), one finds therefore…”

Section: Basic Frameworkmentioning

confidence: 96%

“…The recent developments on the applications of the Bondi-Metzner-Sachs (hereafter BMS) group, i.e., the asymptotic symmetry group of an asymptotically flat space-time (see Equations (A1)-(A3) of Appendix A), have been motivated by black hole physics, quantum gravity and gauge theories, as is well described in many outstanding works (e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. However, a purely classical investigation may still lead to a neater understanding of the mathematical operations frequently performed.…”

Section: Introductionmentioning

confidence: 99%

On the Nature of Bondi–Metzner–Sachs Transformations

Mirzaiyan

Esposito

2023

Symmetry

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This paper investigates, as a first step, the four branches of BMS transformations, motivated by the classification into elliptic, parabolic, hyperbolic and loxodromic proposed a few years ago in the literature. We first prove that to each normal elliptic transformation of the complex variable ζ used in the metric for cuts of null infinity, there is a corresponding BMS supertranslation. We then study the conformal factor in the BMS transformation of the u variable as a function of the squared modulus of ζ. In the loxodromic and hyperbolic cases, this conformal factor is either monotonically increasing or monotonically decreasing as a function of the real variable given by the modulus of ζ. The Killing vector field of the Bondi metric is also studied in correspondence with the four admissible families of BMS transformations. Eventually, all BMS transformations are re-expressed in the homogeneous coordinates suggested by projective geometry. It is then found that BMS transformations are the restriction to a pair of unit circles of a more general set of transformations. Within this broader framework, the geometry of such transformations is studied by means of its Segre manifold.

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“…For instance, unitary representations of asymptotic symmetries [62][63][64][65][66][67][68] and their relation to bulk metrics through coadjoint orbits and geometric actions [69][70][71][72][73][74][75][76][77][78] are well established in both situations, as is the Cardyology of black holes and cosmological solutions [79][80][81]. No such control is available in the 4D realm, where the study of coadjoint orbits [82] and geometric actions [83,84] is in its infancy, and mostly limited to the sector without radiation.…”

Section: Introductionmentioning

confidence: 99%

Radiative asymptotic symmetries of 3D Einstein-Maxwell theory

Bosma,

Geiller,

Majumdar

et al. 2024

SciPost Phys.

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We study the null asymptotic structure of Einstein-Maxwell theory in three-dimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits a massless photon and can therefore accommodate electromagnetic radiation. We derive fall-off conditions for the Maxwell field that contain both Coulombic and radiative modes with non-vanishing news. The latter produces non-integrability and fluxes in the asymptotic surface charges, and gives rise to a non-trivial 3D Bondi mass loss formula. The resulting solution space is thus analogous to a dimensional reduction of 4D pure gravity, with the role of gravitational radiation played by its electromagnetic cousin. We use this simplified setup to investigate choices of charge brackets in detail, and compute in particular the recently introduced Koszul bracket. When the latter is applied to Wald-Zoupas charges, which are conserved in the absence of news, it leads to the field-dependent central extension found earlier in [Class. Quantum Gravity 32, 245001 (2015)]. We also consider (Anti-)de Sitter asymptotics to further exhibit the analogy between this model and 4D gravity with leaky boundary conditions.

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Geometric action for extended Bondi-Metzner-Sachs group in four dimensions

Cited by 17 publications

References 71 publications

Circuit Complexity for Carrollian Conformal (BMS) Field Theories

Circuit Complexity for Carrollian Conformal (BMS) Field Theories

On the Nature of Bondi–Metzner–Sachs Transformations

Radiative asymptotic symmetries of 3D Einstein-Maxwell theory

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