Asymptotic symmetries of three-dimensional higher-spin gravity: the metric approach

Dec 21, 2014
74 pages
Published in:
  • JHEP 03 (2015) 143
  • Published: Mar 26, 2015
e-Print:

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Abstract: (Springer)
The asymptotic structure of three-dimensional higher-spin anti-de Sitter gravity is analyzed in the metric approach, in which the fields are described by completely symmetric tensors and the dynamics is determined by the standard Einstein-Fronsdal action improved by higher order terms that secure gauge invariance. Precise boundary conditions are given on the fields. The asymptotic symmetries are computed and shown to form a non-linear W -algebra, in complete agreement with what was found in the Chern-Simons formulation. The W -symmetry generators are two-dimensional traceless and divergenceless rank-s symmetric tensor densities of weight s (s = 2, 3, · · · ), while asymptotic symmetries emerge at infinity through the conformal Killing vector and conformal Killing tensor equations on the two-dimensional boundary, the solution space of which is infinite-dimensional. For definiteness, only the spin 3 and spin 4 cases are considered, but these illustrate the features of the general case: emergence of the W -extended conformal structure, importance of the improvement terms in the action that maintain gauge invariance, necessity of the higher spin gauge transformations of the metric, role of field redefinitions.
Note:
  • 74 pages. References amended and typos corrected. Version to appear in JHEP
  • Higher Spin Gravity
  • Field Theories in Lower Dimensions
  • Higher Spin Symmetry
  • Conformal and W Symmetry
  • invariance: gauge
  • dimension: 3
  • dimension: 2
  • transformation: gauge
  • density: tensor
  • tensor: Killing