A Grassmann path from to flat space
Dec 10, 2013
Citations per year
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
References(26)
Figures(1)
- [1]
- [2]
- [3]
- [4]
- [5]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [14]
- [15]
- [16]
- [17]
- [18]
- [19]
- [20]
- [21]
- [22]
- [23]
- [24]
- [25]