Light States in Chern-Simons Theory Coupled to Fundamental Matter

TL;DR

The paper investigates SU(N) Chern-Simons theory at large $N$ with fundamental matter on spatial manifolds, emphasizing a torus geometry where light states emerge at small $\lambda=N/k$ with gaps $\Delta \sim \sqrt{\lambda}/N$ (free scalar) or $\Delta \sim \lambda/N$ (critical scalar/fermion) and entropy $S \sim N\log(k)$. By reducing to the low-energy quantum mechanics on flat connections and performing perturbative analyses in the singlet sector, it demonstrates that these light states persist and that odd-order perturbations vanish, with the leading gap controlled by $\Delta \approx \hbar/(2\omega)$. The results imply a breakdown of a purely Vasiliev-gravity description and point to the necessity of including stringy or topological string degrees of freedom to account for topology-dependent entropy, especially at higher genus where $S \sim N^2 \log(k)$. The work also discusses connections to ABJM-type theories, the role of modular invariance, RG flows, and potential condensed matter applications, highlighting a rich interplay between topology, holography, and bulk dynamics beyond traditional higher-spin gravity. Overall, the paper identifies new light topological states and argues for a more complete bulk dual that incorporates extended degrees of freedom beyond the Vasiliev framework.

Abstract

Motivated by developments in vectorlike holography, we study SU(N) Chern-Simons theory coupled to matter fields in the fundamental representation on various spatial manifolds. On the spatial torus T^2, we find light states at small `t Hooft coupling λ=N/k, where k is the Chern-Simons level, taken to be large. In the free scalar theory the gaps are of order \sqrt λ/N and in the critical scalar theory and the free fermion theory they are of order λ/N. The entropy of these states grows like N Log(k). We briefly consider spatial surfaces of higher genus. Based on results from pure Chern-Simons theory, it appears that there are light states with entropy that grows even faster, like N^2 Log(k). This is consistent with the log of the partition function on the three sphere S^3, which also behaves like N^2 Log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.