Light States in Chern-Simons Theory Coupled to Fundamental Matter

TL;DR

This paper investigates light states in SU(N) Chern-Simons theory coupled to matter, revealing their entropy growth and implications for holography and bulk dynamics beyond Vasiliev gravity.

Contribution

It identifies and characterizes light states in Chern-Simons matter theories on various manifolds, highlighting their entropy scaling and the need for extended bulk theories.

Findings

Light states appear at small 't Hooft coupling on T^2.

Entropy of states scales as N Log(k).

Higher genus surfaces suggest even faster entropy growth.

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 \lambda=N/k, where k is the Chern-Simons level, taken to be large. In the free scalar theory the gaps are of order \sqrt {\lambda}/N and in the critical scalar theory and the free fermion theory they are of order \lambda/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.