A Grassmann path from AdS3AdS_3 to flat space

Dec 10, 2013
20 pages
Published in:
  • JHEP 03 (2014) 036
  • Published: 2014
e-Print:

Citations per year

20132016201920222023051015
Abstract: (arXiv)
We show that interpreting the inverse AdS_3 radius 1/l as a Grassmann variable results in a formal map from gravity in AdS_3 to gravity in flat space. The underlying reason for this is the fact that ISO(2,1) is the Inonu-Wigner contraction of SO(2,2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS_3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS_3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.
Note:
  • 20 pages, 1 figure; v2: many refs added, minor changes, v3: typos fixed, one more ref added, JHEP version
  • AdS-CFT Correspondence
  • Chern-Simons Theories
  • Classical Theories of Gravity
  • Conformal and W Symmetry
  • spin: high
  • algebra: Virasoro
  • vector: Killing
  • anti-de Sitter
  • gravitation
  • Grassmann