Chern–Simons theory with vector fermion matter

By S. Giombi, Shiraz Minwalla, Shiroman Prakash, S. Trivedi, S. Wadia, Xi Yin. 2011

503 citations recorded by the source corpus.

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 |λ|=1; the conformal theory does not exist for |λ|>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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3564f9be31ebf84f7f170305b4885e8b2e596264

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Eric Perlmutter
2. M. Gaberdiel
3. Rajesh Gopakumar
4. S. Giombi
5. Per Kraus
6. O. Aharony
7. I. Klebanov
8. Xi Yin

In Nuclear and High Energy Physics

1. S. Giombi
2. Eric Perlmutter
3. Rajesh Gopakumar
4. M. Gaberdiel
5. I. Klebanov
6. O. Aharony
7. Xi Yin
8. J. Maldacena

Citations in the corpus

• On the uniqueness of higher-spin symmetries in AdS and CFT (2013, unknown): “is realized through a Chern-Simons term, [63].”
• Particle-Vortex Duality from 3D Bosonization (2016, background): “[20,21] strongly suggest that if we take the free fermion as the left-hand side of Eq.”
• How higher-spin gravity surpasses the spin-two barrier (2010, background): “27 For instance, the conjecture has been generalised in the presence of a Chern-Simons gauge field on the three-dimensional boundary [153, 154].”
• d = 3 bosonic vector models coupled to Chern-Simons gauge theories (2011, background): “It has a unique parity-violating tensor structure, and to compute its coefficient it will prove useful (as in [38]) to choose all polarizations equal and null, εi = ε, ε 2 = 0, and to take the limit x2 → x1.”
• Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, background): “Recently, a convergence of ideas from condensed matter physics [1-6], supersymmetric quantum field theory [7-19], and string theory [20-34] has led to a large set of new boson/fermion dualities [35-45] and new fermion/fermion dualities [46,38,39,47,45].”
• Convexity and liberation at large spin (2012, background): “On the boundary sometimes it is possible to use the constraints to get some general predictions [60,61,62].”
• The higher spin/vector model duality (2012, methodology): “A two-loop calculation of correlation functions [11], an exact calculation in the Chern-Simons-scalar vector model at large N [20], combined with arguments of [19,14] suggests that the identification between θ0 and λ is simply”
• ABJ triality: from higher spin fields to strings (2012, methodology): “in the singlet sector. Substantial evidence for these conjectures has been provided by comparison of three-point functions [4, 5], and analysis of higher spin symmetries [6, 7, 8, 9]. It was noted in [10, 11] that, at large N, the free O(N) and U(N) theories described above each have a family of one”
• Remarks on the Sachdev-Ye-Kitaev model (2016, methodology): “This model is structurally reminiscent of the 2+1 dimensional O(N) theories with fundamental bosons and fermions studied in [36].”
• Correlators of large N fermionic Chern-Simons vector models (2012, methodology): “For non-zero λ the vanishing of this correlator was predicted in [2] by computations in Vasiliev’s gravity theory and by a perturbative calculation in field theory.”
• Bounding the space of holographic CFTs with chaos (2016, background): “These are famously dual to O(N) vector models in d ≥ 3 CFT dimensions (and, in d = 3, Chern-Simons deformations thereof [29, 30]).”
• AdS description of induced higher-spin gauge theory (2013, background): “These theories have been conjectured to be dual to 3-d CFTs such as the critical O(N) model [16], or the Gross-Neveu model [17,18], or various large N Chern-Simons theories coupled to conformal matter in the fundamental representation of the gauge group [19, 20].”
• Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, methodology): “The results of [20] for even contributions to correlators imply that in this mapping λ̃ = tan(θ), and this is confirmed by more detailed computations in [25].”