@article{84f29c5d651a46c092a74c909bca9d58,

title = "Chern-Simons theory with vector fermion matter",

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.",

author = "Simone Giombi and Shiraz Minwalla and Shiroman Prakash and Trivedi, {Sandip P.} and Wadia, {Spenta R.} and Xi Yin",

note = "Funding Information: We are grateful to Ofer Aharony and Rajesh Gopakumar for crucial discussions that led to the formulation of some of the questions addressed in this paper. We would like to acknowledge Sayantani Bhattacharyya, Jyotirmoy Bhattacharya and V. Umesh for collaboration at various stages of this project. We thank O. Aharony and J. Bhattacharya for comments on the manuscript. We would also like to acknowledge useful discussions with C.-M. Chang, K. Damle, J. David, A. Dhar, S. Dutta, D. Hofman, N. Iizuka, D. Jafferis, S. Kim, S.S. Lee, G. Mandal, K. Papadodimas, M. Rangamani, S. Sachdev, A. Sen, C. Sonnenshein and E. Witten. S.G. is supported by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. The work of S.M. was supported by a Swarnajayanti fellowship. The work of S.M., S.P., S.T. and S.W. was supported by the DAE, government of India. S.G. would like to thank Princeton U., the Simons Center for Geometry and Physics, Mc Gill U., the Weizmann Institute, the organizers of the PhyMSI conference in Cargese and of the Simons Summer Workshop in Mathematics and Physics 2011 for hospitality during completion of this work. S.M. would like to thank the Weizmann Institute, Cambridge University, KIAS, ICTP, the organizers of GR19, PASCOS 2010, and the Indian Strings Meeting (ISM) 2011 for their hospitality while this work was in progress. S.P. would like to thank the organizers of ISM 2011, and the Centre for High Energy Physics, Indian Institute of Science, Bangalore for their hospitality. X.Y. would like to thank the organizers of GR19 and of ISM 2011, Tata Institute of Fundamental Research, Berkeley Center for Theoretical Physics, Simons Center for Geometry and Physics, Fields Institute, and Aspen Center for Physics for their hospitality. The work of X.Y. was supported by the Fundamental Laws Initiative Fund at Harvard University and in part by NSF Award PHY-0847457. S.M., S.P., S.T. and S.W. would also like to acknowledge our debt to the people of India for their generous and steady support to research in the basic sciences. ",

year = "2012",

month = aug,

doi = "10.1140/epjc/s10052-012-2112-0",

language = "English (US)",

volume = "72",

pages = "1--65",

journal = "European Physical Journal C",

issn = "1434-6044",

publisher = "Springer New York",

number = "8",

}