BMS 4 algebra, its stability and deformations
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Springer
Received: February 23, 2019 Accepted: April 2, 2019 Published: April 9, 2019
H.R. Safari and M.M. Sheikh-Jabbari School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
E-mail: [email protected], [email protected] Abstract: We continue analysis of [1] and study rigidity and stability of the bms4 ald 4 . We construct and classify the family of gebra and its centrally extended version bms algebras which appear as deformations of bms4 and in general find the four-parameter family of algebras W(a, b; a ¯, ¯b) as a result of the stabilization analysis, where bms4 = W(−1/2, −1/2; −1/2, −1/2). We then study the W(a, b; a ¯, ¯b) algebra, its maximal finite subgroups and stability for different values of the four parameters. We prove stability of the W(a, b; a ¯, ¯b) family of algebras for generic values of the parameters. For special cases of (a, b) = (¯ a, ¯b) = (0, 0) and (a, b) = (0, −1), (¯ a, ¯b) = (0, 0) the algebra can be deformed. In particular we show that centrally extended W(0, −1; 0, 0) algebra can be deformed to an algebra which has three copies of Virasoro as a subalgebra. We briefly discuss these deformed algebras as asymptotic symmetry algebras and the physical meaning of the stabilization and implications of our result. Keywords: Conformal and W Symmetry, Gauge-gravity correspondence, Space-Time Symmetries ArXiv ePrint: 1902.03260
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)068
JHEP04(2019)068
BMS4 algebra, its stability and deformations
Contents 1 Introduction and motivations
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2 Introduction to bms4 algebra 2.1 4d flat space asymptotic symmetry algebra 2.2 More on global part of the bms4 algebra 2.3 AdS4 isometry, so(3, 2) algebra
5 5 6 7 8 8 10 13
4 Most general formal deformations of bms4 algebra 4.1 Integrability, obstructions and formal deformation.
14 15
5 On 5.1 5.2 5.3
W(a, b; a ¯, ¯ b) algebra, its subalgebras and deformations Subalgebras of W(a, b; a ¯, ¯b) Deformations of generic W(a, b; a ¯, ¯b) algebra Deformations of special W algebras
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c 6 Deformation of centrally extended W(a, b; a ¯, ¯ b) algebra, W(a, b; a ¯, ¯ b) ¯ 6.1 Most general deformations of centrally extended W(a, b; a ¯, b) algebra ¯ 6.2 Most general deformations of specific points in (a, b; a ¯, b) space
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7 Cohomological consideration of W(a, b; a ¯, ¯ b) algebra 7.1 Cohomological consideration of bms4 algebra d 4 algebra 7.2 Cohomological consideration for bms 7.3 Cohomological consideration of W(a, b; a ¯, ¯b) algebra
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8 Summary and concluding remarks
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A Algebra generators as functions on celestial two sphere
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B Hochschild-Serre spectral sequence
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1
Introduction and motivations
Motivated by a possible resolution to black hole information paradox and also by a rederivation and reinterpretation of soft theorems, studying algebras of “soft charges” has attracted a lot of attention, see [2–4] and references therein or their citations list. Soft charges ar
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