2014/12/21 by Andrea Campoleoni, Campoleoni, Andrea, Marc Henneaux +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1412.6774
The asymptotic structure of three-dimensional higher-spin anti-de Sitter\ngravity is analyzed in the metric approach, in which the fields are described\nby completely symmetric tensors and the dynamics is determined by the standard\nEinstein-Fronsdal action improved by higher order terms that secure gauge\ninvariance. Precise boundary conditions are given on the fields. The asymptotic\nsymmetries are computed and shown to form a non-linear W-algebra, in complete\nagreement with what was found in the Chern-Simons formulation. The W-symmetry\ngenerators are two-dimensional traceless and divergenceless rank-s symmetric\ntensor densities of weight s (s = 2, 3, ...), while asymptotic symmetries\nemerge at infinity through the conformal Killing vector and conformal Killing\ntensor equations on the two-dimensional boundary, the solution space of which\nis infinite-dimensional. For definiteness, only the spin 3 and spin 4 cases are\nconsidered, but these illustrate the features of the general case: emergence of\nthe W-extended conformal structure, importance of the improvement terms in the\naction that maintain gauge invariance, necessity of the higher spin gauge\ntransformations of the metric, role of field redefinitions.\n