1111.2834 (H. S. Tan)

Aspects of Three-dimensional Spin-4 Gravity    [PDF]

H. S. Tan

We discuss some interesting holographical aspects of three-dimensional
higher-spin gravity with a negative cosmological constant in the framework of
SL(4, R) \times SL(4, R) Chern-Simons theory. Using a recently found technique,
we construct explicitly a solution that can be interpreted as spin-4
generalization of the BTZ solution, and demonstrate how W_4 symmetry and the
higher-spin Ward identities arise from the bulk equations of motion coupled to
spin-3 and spin-4 currents. We match the eigenvalues of a Wilson loop along the
time-like direction of the BTZ to that of the spin-4 solution, and show that
this yields remarkably consistent gravitational thermodynamics for the latter.
This furnishes an important, concrete supporting example for a recent proposal
to understand spacetime geometries in three-dimensional higher-spin gravity
formulated via SL(N, R) \times SL(N, R) Chern-Simons theories.

View original: http://arxiv.org/abs/1111.2834