Light States in Chern-Simons Theory Coupled to Fundamental Matter

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.

58 pages, LaTeX, no figures, Minor error corrected, references added, The main results of the paper have not changed

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