Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations

Abstract

This thesis is devoted to the study of the deformation and rigidity of infinite dimensional Lie algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider $bm{s}_3$, Virasoro-Kac-Moody and $bm{s}_4$ algebras and their central extensions which are respectively obtained as asymptotic and/or near horizon symmetry algebras for Einstein gravity on $3d$ flat, AdS${}_3$ and $4d$ flat spacetimes. We also explore possible deformations of the Maxwell-BMS algebra, which is obtained as asymptotic symmetry algebra of the Chern-Simons gravity theory invariant under the $2+1$ dimensional Maxwell algebra. We find that these algebras are not rigid and can be deformed into new non isomorphic infinite dimensional (family of) algebras. We study these deformations by direct computations and also by cohomological analysis. We then classify all the algebras obtained through deformation of these algebras as well as all possible central extensions thereof. We propose/conjecture an extension of the Hochschild-Serre factorization theorem for infinite dimensional algebras as well as introducing a new notion of rigidity for family algebras obtained through deformation. We also explore physical realizations and significance of the family of algebras we obtain through the deformation procedure.

171 pages, doctoral thesis (2020)

References in corpus (26)

• The BMS/GCA correspondence
• Flat Holography: Aspects of the dual field theory
• Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity
• Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions
• Generalized cosmological term from Maxwell symmetries
• Deformations of Maxwell algebra and their Dynamical Realizations
• Remarks on l-conformal extension of the Newton-Hooke algebra
• Higher Spin Black Holes with Soft Hair
• On AdS/CFT of Galilean Conformal Field Theories
• N=1 Supergravity and Maxwell superalgebras
• Geometric actions and flat space holography
• Note on the First Law with p-form potentials
• Two Virasoro symmetries in stringy warped AdS${}_3$
• Generalized Poincare algebras and Lovelock-Cartan gravity theory
• Minimal D=4 supergravity from the superMaxwell algebra
• Spontaneously Broken 3d Hietarinta/Maxwell Chern-Simons Theory and Minimal Massive Gravity
• Generalized Pure Lovelock Gravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Horizons 2020
• Asymptotic Symmetries of Maxwell Chern-Simons Gravity with Torsion
• On the addition of torsion to chiral gravity
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Asymptotic behaviour of Maxwell fields in higher dimensions
• The derivations, central extensions and automorphism group of the Lie algebra $W$
• Sliding Surface Charges on AdS${}_3$
• Lie algebras : Classification, Deformations and Rigidity

Cited by in corpus (2)

• Holography and black holes in asymptotically flat FLRW
• On deformations and extensions of $\text{Diff}(S^2)$