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Light states in Chern-Simons theory coupled to fundamental matter

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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 \( \sqrt{\lambda }/N \) 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.

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Authors and Affiliations

  1. Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA, 94305-4060, U.S.A

    Shamik Banerjee, Jonathan Maltz & Stephen H. Shenker

  2. Kavli IPMU, The University of Tokyo Kashiwa, Chiba, 277-8583, Japan

    Simeon Hellerman

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Banerjee, S., Hellerman, S., Maltz, J. et al. Light states in Chern-Simons theory coupled to fundamental matter. J. High Energ. Phys. 2013, 97 (2013). https://doi.org/10.1007/JHEP03(2013)097

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