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arXiv · 2511.03105

BPS phases and fortuity in higher spin holography

Seok Kim·Jehyun Lee·Siyul Lee·Hyunwoo Oh
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Abstract

We study the BPS states of $U(N)_k\times U(1)_{-k}$ vector Chern-Simons theory on a sphere at weak coupling $\lambda=\frac{N}{k}\ll 1$, dual to an AdS$_4$ higher spin gravity. Higher spin currents are well known to be anomalous at $\lambda\neq 0$. 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.

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Seok Kim, Jehyun Lee, Siyul Lee, Hyunwoo Oh. 2025-11-05. BPS phases and fortuity in higher spin holography. https://doi.org/10.1007/jhep07(2026)218

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