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Register a new user3-dimensional $Lambda$-BMS Symmetry and its Deformations
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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.
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Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of superconformal groups SU(2,2|N) and OSp(8*|2n) in four and six dimensions were constructed as minreps and their U(1) and SU(2) deformations, respectively. In this paper we extend these results to SU(2) deformations of the minrep of N=4 superconformal algebra D(2,1;lambda) in one dimension. We find that SU(2) deformations can be achieved using n pairs of bosons and m pairs of fermions simultaneously. The generators of deformed minimal representations of D(2,1;lambda) commute with the generators of a dual superalgebra OSp(2n*|2m) realized in terms of these bosons and fermions. We show that there exists a precise mapping between symmetry generators of N=4 superconformal models in harmonic superspace studied recently and minimal unitary supermultiplets of D(2,1;lambda) deformed by a pair of bosons. This can be understood as a particular case of a general mapping between the spectra of quantum mechanical quaternionic Kahler sigma models with eight super symmetries and minreps of their isometry groups that descends from the precise mapping established between the 4d, N=2 sigma models coupled to supergravity and minreps of their isometry groups.
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.
We present the quantum $kappa$-deformation of BMS symmetry, by generalizing the lightlike $kappa$-Poincare Hopf algebra. On the technical level, our analysis relies on the fact that the lightlike $kappa$-deformation of Poincare algebra is given by a twist and the lightlike deformation of any algebra containing Poincare as a subalgebra can be done with the help of the same twisting element. We briefly comment on the physical relevance of the obtained $kappa$-BMS Hopf algebra as a possible asymptotic symmetry of quantum gravity.
In this work, we revisit unitary irreducible representations of the Bondi-Metzner-Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of super-momenta in addition to four-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing four-momentum, which may nevertheless be produced by scattering of particle-like states. This fact has interesting implications for the S-matrix in gravitational theories.
Motivated by the BPS/CFT correspondence, we explore the similarities between the classical $beta$-deformed Hermitean matrix model and the $q$-deformed matrix models associated to 3d $mathcal{N}=2$ supersymmetric gauge theories on $D^2times_{q}S^1$ and $S_b^3$ by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the $W$-algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.
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