BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Abstract BMS symmetry is a symmetry of asymptotically flat spacetimes in vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincaré subalgebras, a fact that has previously been noted in the 3 dimensional case only. Then we use these subalgebras to construct an infinite number of different Hopf algebras being quantum deformations of the BMS algebras. We also discuss different types of twist-deformations and the dual Hopf algebras, which could be interpreted as noncommutative, extended quantum spacetimes.

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Holographic symmetry algebras for gauge theory and gravity

Journal of High Energy Physics ◽

10.1007/jhep11(2021)152 ◽

2021 ◽

Vol 2021 (11) ◽

Author(s):

A. Guevara ◽

E. Himwich ◽

M. Pate ◽

A. Strominger

Keyword(s):

Gauge Theory ◽

Infinite Number ◽

Symmetry Algebra ◽

Complete Classification ◽

Asymptotically Flat ◽

Gravitational Theories ◽

Closed Subalgebra ◽

Flat Spacetimes ◽

Celestial Sphere

Abstract All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

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BMS field theories and Weyl anomaly

Journal of High Energy Physics ◽

10.1007/jhep07(2021)101 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Arjun Bagchi ◽

Sudipta Dutta ◽

Kedar S. Kolekar ◽

Punit Sharma

Keyword(s):

Three Dimensions ◽

Field Theories ◽

Partition Functions ◽

Two Dimensional ◽

Speed Of Light ◽

Asymptotically Flat ◽

Weyl Invariance ◽

Flat Spacetimes ◽

Liouville Action ◽

Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

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Soft photon theorem in the small negative cosmological constant limit

Journal of High Energy Physics ◽

10.1007/jhep08(2021)105 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Nabamita Banerjee ◽

Karan Fernandes ◽

Arpita Mitra

Keyword(s):

Cosmological Constant ◽

Tree Level ◽

Leading Order ◽

Asymptotically Flat ◽

Soft Factor ◽

Flat Spacetime ◽

Electromagnetic Interactions ◽

Flat Spacetimes ◽

Perturbative Corrections ◽

Soft Factors

Abstract We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l. This identifies 1/l2 perturbative corrections to the known asymptotically flat spacetime leading and subleading soft factors. Our analysis is only valid to leading order in 1/l2. The leading soft factor can be expected to be universal and holds beyond tree level. This allows us to derive a 1/l2 corrected Ward identity, following the known equivalence between large gauge Ward identities and soft theorems in asymptotically flat spacetimes.

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Observations of Hawking radiation: the Page curve and baby universes

Journal of High Energy Physics ◽

10.1007/jhep04(2021)272 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Donald Marolf ◽

Henry Maxfield

Keyword(s):

Black Holes ◽

Quantum Systems ◽

Late Time ◽

Asymptotically Flat ◽

Black Hole Information ◽

Flat Spacetimes ◽

The Cost ◽

Baby Universes ◽

Time Extrapolation ◽

Asymptotic Observers

AbstractWe reformulate recent insights into black hole information in a manner emphasizing operationally-defined notions of entropy, Lorentz-signature descriptions, and asymptotically flat spacetimes. With the help of replica wormholes, we find that experiments of asymptotic observers are consistent with black holes as unitary quantum systems, with density of states given by the Bekenstein-Hawking formula. However, this comes at the cost of superselection sectors associated with the state of baby universes. Spacetimes studied by Polchinski and Strominger in 1994 provide a simple illustration of the associated concepts and techniques, and we argue them to be a natural late-time extrapolation of replica wormholes. The work aims to be self-contained and, in particular, to be accessible to readers who have not yet mastered earlier formulations of the ideas above.

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Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽

10.3390/sym13081309 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1309

Author(s):

Jerzy Lukierski

Keyword(s):

Phase Space ◽

Hopf Algebras ◽

Deformation Parameter ◽

Heisenberg Algebra ◽

Planck Length ◽

Covariant Quantum ◽

Drinfeld Twist ◽

Quantum Deformations ◽

Heisenberg Double ◽

Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

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Asymptotically Flat Spacetimes

Advanced Lectures on General Relativity - Lecture Notes in Physics ◽

10.1007/978-3-030-04260-8_3 ◽

2019 ◽

pp. 81-102

Author(s):

Geoffrey Compère

Keyword(s):

Asymptotically Flat ◽

Flat Spacetimes

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On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700031918 ◽

1993 ◽

Vol 55 (1) ◽

pp. 41-59 ◽

Cited By ~ 18

Author(s):

Klaus Ecker

Keyword(s):

Mean Curvature ◽

Mean Curvature Flow ◽

A Priori Estimates ◽

A Priori ◽

Curvature Flow ◽

Lorentzian Manifold ◽

Asymptotically Flat ◽

Spacelike Hypersurfaces ◽

Flat Spacetimes ◽

Weaker Conditions

AbstractWe prove a priori estimates for the gradient and curvature of spacelike hypersurfaces moving by mean curvature in a Lorentzian manifold. These estimates are obtained under much weaker conditions than have been previously assumed. We also use mean curvature flow in the construction of maximal slices in asymptotically flat spacetimes. An essential tool is a maximum principle for sub-solutions of a parabolic operator on complete Riemannian manifolds with time-dependent metric.

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Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming

Theory and Practice of Logic Programming ◽

10.1017/s1471068420000411 ◽

2020 ◽

Vol 20 (6) ◽

pp. 942-957

Author(s):

Yusuf Izmirlioglu ◽

Esra Erdem

Keyword(s):

Nonmonotonic Reasoning ◽

Answer Set Programming ◽

3 Dimensional ◽

3D Space ◽

Formal Framework ◽

Different Types ◽

New Type ◽

Cardinal Directions ◽

Answer Set

AbstractWe propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-NCDC-ASP, and illustrate its usefulness with applications.

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A Knowledge Based Automatic Pipe Routing System

ASME 1992 International Computers in Engineering Conference: Volume 1 — Artificial Intelligence; Expert Systems; CAD/CAM/CAE; Computers in Fluid Mechanics/Thermal Systems ◽

10.1115/cie1992-0017 ◽

1992 ◽

Author(s):

D. Jain ◽

M. Chatterjee ◽

A. Unemori ◽

N. Thangam

Keyword(s):

Dimensional Space ◽

Compact Representation ◽

Routing Problem ◽

3 Dimensional ◽

Intelligent Search ◽

Knowledge Based ◽

Embedded Design ◽

Pipe Routing ◽

Different Types ◽

Significant Attention

Abstract The pipe routing problem, wherein layout of one or more pipes has to be decided in a 3-dimensional space while satisfying several different types of constraints, has attracted significant attention recently. This paper describes a knowledge-based automated pipe routing system which generates practical routes that meet several diverse criteria. The system employs intelligent search (with embedded design constraints) upon a compact representation of the free space in a facility, thus avoiding expensive interference checks and adjustments that must be performed in some of the other systems.

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