BPS phases and fortuity in higher spin holography

A bstract We study the BPS states of U ( N ) k × U (1) − k vector Chern-Simons theory on a sphere at weak coupling λ = $$ \frac{N}{k} $$ N k ≪ 1, dual to an AdS 4 higher spin gravity. Higher spin currents are well known to be anomalous at λ ≠ 0. We show that these non-BPS higher spin particles form multi-particle ‘BPS bounds’ at low energy, and interpret them as a primordial form of small black hole states. We also construct a new heavy BPS operator at N = 2. We study the BPS phases of this system from the large N index at Planckian ‘temperatures’. The deconfined saddles at high temperature exist only above a threshold, similar to the BTZ black holes. The low temperature saddles are given by novel 2-cut eigenvalue distributions. Their phase transition involves subtle issues like the holomorphic anomaly and the background independence, whose studies we initiate. In particular, we obtain a lower bound on the critical temperature by studying the eigenvalue instantons.