Light States in Chern-Simons Theory Coupled to Fundamental Matter

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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 T², 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 √ 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 N² Log(k). This is consistent with the log of the partition function on the three sphere S³, which also behaves like N² Log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.