2019/09/30 by P. Concha, H. R. Safari
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebra representation #Black Holes and Theoretical Physics #Current algebra #Filtered algebra #Ideal (ethics) #Noncommutative and Quantum Gravity Theories #Rigidity (electromagnetism) #Stability (learning theory) #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep04(2020)073
published as JHEP 04 (2020) 073 · 27 pages
openalex created_date 2019/10/03 · arxiv created 2020/03/31 · openalex publication_date 2020/04/01 · arxiv updated 2020/04/17 · openalex updated_date 2026/08/05
A bstract In this work we present different infinite dimensional algebras which appear as deformations of the asymptotic symmetry of the three-dimensional Chern-Simons gravity for the Maxwell algebra. We study rigidity and stability of the infinite dimensional enhancement of the Maxwell algebra. In particular, we show that three copies of the Witt algebra and the \mathfrakbms3⊕ \mathfrakwitt <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>bms</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>⊕</mml:mo> <mml:mtext>witt</mml:mtext> </mml:math> algebra are obtained by deforming its ideal part. New family of infinite dimensional algebras are obtained by considering deformations of the other commutators which we have denoted as M ( a, b ; c, d ) and M(α,β;ν) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mover> <mml:mi>α</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mover> <mml:mi>β</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mfenced> </mml:math> . Interestingly, for the specific values a = c = d = 0 , b=-(1)/(2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> the obtained algebra M(0,-(1)/(2);0,0) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> <mml:mfenced> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> <mml:mn>0</mml:mn> <mml:mn>0</mml:mn> </mml:mfenced> </mml:math> corresponds to the twisted Schrödinger-Virasoro algebra. The central extensions of our results are also explored. The physical implications and relevance of the deformed algebras introduced here are discussed along the work.