Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBMS algebras in 4 and 3 dimensions, their quantum deformations and duals
79
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
BMS symmetry is a symmetry of asymptotically flat spacetimes in the 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 Poincare 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.
rate research
Read More
In this paper, we study quantum group deformations of the infinite-dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite-dimensional subalgebras we classify all possible Lie bialgebra structures and for selected examples, we explicitly construct the related Hopf algebras. Using cohomological arguments we show that this construction can always be performed by a so-called twist deformation. The resulting structures can be compared to the well-known $kappa$-Poincare Hopf algebras constructed on the finite-dimensional Poincare or (anti) de Sitter algebra. The dual $kappa$ Minkowski spacetime is supposed to describe a specific non-commutative geometry. Importantly, we find that some incarnations of the $kappa$-Poincare can not be extended consistently to the infinite-dimensional algebras. Furthermore, certain deformations can have potential physical applications if subalgebras are considered. The presence of the full symmetry algebra might have observable consequences that could be used to rule out these deformations.
Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary vacuum transition induced by the scattering process.
We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $mathbb{R}times S^{d-1}$ and ${rm AdS}_2times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call `superdilations. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/CFT correspondence, we propose a bulk holographic description in semi-classical gravity that reproduces the results obtained from CFT computations. We discuss the implications of our results regarding quantum hairs of asymptotically flat (near-)extremal black holes.
Interacting quantum scalar field theories in $dS_Dtimes M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the critical behavior of Euclidean $lambdaphi_4^4$ theory in the symmetric phase and find the asymptotic behavior $beta(lambda)sim lambda$ of the beta function at strong coupling. Scaling violating contributions to the beta function are also estimated in this regime.
By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $Lambda$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of $so_q(4)$, with $ q = exp{(ihbar sqrt{Lambda}/2kappa)}$. By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping $kappa$ finite, we obtain the kappa-Poincare algebra of the flat quantum space-time symmetries.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
