Quantum W-symmetry in AdS_3

Understand

It has recently been argued that, classically, massless higher spin theories in AdS_3 have an enlarged W_N-symmetry as the algebra of asymptotic isometries.

• In this note we provide evidence that this symmetry is realised (perturbatively) in the quantum theory.
• We perform a one loop computation of the fluctuations for a massless spin $s$ field around a thermal AdS_3 background.
• The resulting determinants are evaluated using the heat kernel techniques of arXiv:0911.5085.