2020/08/31 by Alejandra Castro, Alberto Faraggi, Israel Osorio +1
Mathematics · Physics and Astronomy · #Algebra over a field #Basis (linear algebra) #Black Holes and Theoretical Physics #Boundary (topology) #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Flow (mathematics) #Geometry #Holography #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Minor (academic) #Multiplet #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Signature (topology) #Spectral line #Superalgebra #Supergravity #Supersymmetry #Symmetry (geometry) #Theoretical physics #hep-th
paper · pdf · doi:10.1007/jhep12(2020)177
published as JHEP 12 (2020) 177 · 42 pages, 4 tables
openalex created_date 2020/08/18 · openalex publication_date 2020/12/01 · arxiv created 2021/01/20 · arxiv updated 2021/01/21 · openalex updated_date 2026/08/05
A bstract This is a long-overdue companion paper to [1]. We study the relation between sl (3 | 2) Chern-Simons supergravity on AdS 3 and two-dimensional CFT’s with N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 super- W3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward identities. By imposing suitable hermiticity conditions on the CFT currents, we identify the superalgebra su (2 , 1 | 1 , 1) as the appropriate real form of sl (3 | 2) in Lorentzian signature. We take the opportunity to review some of the properties of the N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 super- W3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> conformal algebra, including its multiplet structure, OPE’s and spectral flow invariance, correcting some minor typos present in the literature.