Infinite distances in multicritical CFTs and higher-spin holography

TL;DR

This paper explores the swampland distance conjecture in higher-spin gravity, revealing that infinite-distance limits in vector models lead to power-like decay, contrasting with the exponential decay typical of matrix-like gauge theories.

Contribution

It demonstrates that in multicritical vector models, the quantum information distance exhibits power-like decay, challenging the expectation of exponential decay in higher-spin limits.

Findings

Infinite-distance limits lead to power-like decay in vector models.

Stringy exponential decay is characteristic of matrix-like gauge theories.

Higher-spin limits in vector models differ from matrix models in decay behavior.

Abstract

We investigate the swampland distance conjecture in higher-spin gravity. To this end, we study multicritical generalizations of large-$N$ vector models, bosonic and fermionic, and we compute the quantum information distance along selected renormalization-group trajectories toward the higher-spin limit. In striking contrast to the expected exponential decay of higher-spin masses or anomalous dimensions, we find that infinite-distance limits in these models lead to a power-like decay. This suggests that stringy exponential decays are characteristic of matrix-like gauge theories, rather than vector models. We corroborate this notion studying the information distance along coupling variations in Chern-Simons-matter CFTs, where matrix-like degrees of freedom dominate over vector-like ones.