Chemical potentials in three-dimensional higher spin anti-de Sitter gravity

Understand

We indicate how to introduce chemical potentials for higher spin charges in higher spin anti-de Sitter gravity in a manner that manifestly preserves the original asymptotic W-symmetry.

• This is done by switching on a non-vanishing component of the connection along the temporal (thermal) circles.
• We first recall the procedure in the pure gravity case (no higher spin) where the only "chemical potentials" are the temperature and the chemical potential associated with the angular momentum.
• We then generalize to the higher spin case.