Light states in Chern-Simons theory coupled to fundamental matter

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 root 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.