Chern-Simons theory with vector fermion matter

Simone Giombi, Shiraz Minwalla, Shiroman Prakash, Sandip P. Trivedi, Spenta R. Wadia, Xi Yin

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Abstract

We study three-dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on ℝ2 as a function of the 't Hooft coupling λ=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at {pipe}λ{pipe}=1; the conformal theory does not exist for {pipe}λ{pipe}>1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.

Original languageEnglish (US)
Article number2112
Pages (from-to)1-65
Number of pages65
JournalEuropean Physical Journal C
Volume72
Issue number8
DOIs
StatePublished - Aug 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Engineering (miscellaneous)
  • Physics and Astronomy (miscellaneous)

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    Giombi, S., Minwalla, S., Prakash, S., Trivedi, S. P., Wadia, S. R., & Yin, X. (2012). Chern-Simons theory with vector fermion matter. European Physical Journal C, 72(8), 1-65. [2112]. https://doi.org/10.1140/epjc/s10052-012-2112-0