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Chern-Simons Theory with Vector Fermion Matter | | Simone Giombi
; Shiraz Minwalla
; Shiroman Prakash
; Sandip P. Trivedi
; Spenta R. Wadia
; Xi Yin
; | | Date: |
19 Oct 2011 | | 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 lightcone gauge, we
compute the exact planar free energy of the theory at finite temperature on R^2
as a function of the ’t Hooft coupling lambda=N/k. Employing a dimensional
reduction regularization scheme, we find that the free energy vanishes at
|lambda|=1; the conformal theory does not exist for |lambda|>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 lightcone Hamiltonian
formulation of this theory where a W-infinity 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. | | Source: | arXiv, 1110.4386 | | Services: | Forum | Review | PDF | Favorites | |
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