From correlators to Wilson loops in Chern-Simons matter theories (original) (raw)
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The Chern-Simons coefficient in supersymmetric Yang-Mills Chern-Simons theories
Physics Letters B, 1996
We study one-loop correction to the Chern-Simons coefficient κ = k/4π in N = 1, 2, 3 supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter k is known to be k → k + c v , where c v is the quadratic Casimir of the gauge group. In the N = 1 case, the fermionic contribution cancels the bosonic contribution by half and the shift is k → k + c v /2, making the theory anomalous if c v is odd. In the N = 2, 3 cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate the mass corrections, showing the supersymmetry is preserved. As the matter fields decouple from the gauge field in the pure Chern-Simons limit, this work sheds some
Journal of High Energy Physics, 2010
Using N = 2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) × SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a fourloop contribution to the function h 2 (λ) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h 2 (λ) that interpolates between weak and strong couplings.
Remarks on N=2 supersymmetric Chern-Simons theories
Physics Letters B, 1992
We discuss the complete superspace formulation of general non-abelian N= 2 supersymmetric Chern-Simons theories. It is shown that the component level spin-0 self-interactions in such models are not completely determined by the superpotential. We compute the anomalous dimensions and beta-functions of the N= 2 supersymmetric non-abelian Chern-Simons theory, when the self-interactions of scalar multiplets are absent. A simple classification of the "soft-breaking terms" of N= 2 supersymmetry is also performed.
Superspace calculation of the four-loop spectrum in supersymmetric Chern-Simons theories
Journal of High Energy Physics
Using superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) × SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h 2(λ) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h 2(λ) that interpolates between weak and strong couplings.
Integrability of N=6 Chern-Simons theory at six loops and beyond
Physical Review D, 2010
We study issues concerning perturbative integrability of N = 6 Chern-Simons theory at planar and weak 't Hooft coupling regime. By Feynman diagrammatics, we derive so called maximalranged interactions in the quantum dilatation generator, originating from homogeneous and inhomogeneous diagrams. These diagrams require proper regularization of not only ultraviolet but also infrared divergences. We first consider standard operator mixing method. We show that homogeneous diagrams are obtainable by recursive method to all orders. The method, however, is not easily extendable to inhomogeneous diagrams. We thus consider two-point function method and study both operator contents and spectrum of the quantum dilatation generator up to six loop orders. We show that, of two possible classes of operators, only one linear combination actually contributes. Curiously, this is exactly the same combination as in N = 4 super Yang-Mills theory. We then study spectrum of anomalous dimension up to six loops. We find that the spectrum agrees perfectly with the prediction based on quantum integrability. In evaluating the six loop diagrams, we utilized remarkable integer-relation algorithm (PSLQ) developed by Ferguson, Baily and Arno.
Integrability of N ¼ 6 Chern-Simons theory at six loops and beyond
We study issues concerning perturbative integrability of N ¼ 6 Chern-Simons theory at planar and weak 't Hooft coupling regime. By Feynman diagrammatics, we derive so-called maximal-ranged interactions in the quantum dilatation generator, originating from homogeneous and inhomogeneous diagrams. The dilatation operator requires proper regularization of ultraviolet and infrared divergences and also bears scheme dependence depending on operator-mixing or two-point function methods adopted. We first consider the standard operator-mixing method. We show that homogeneous diagrams are obtainable by recursive method to all orders. The method, however, is not easily extendable to inhomogeneous diagrams. We thus consider two-point function method and study both operator contents and the spectrum of the quantum dilatation generator up to six-loop orders. Within this scheme, we show that, of two possible classes of operators, only one linear combination actually contributes. Curiously, this is exactly the same combination as in N ¼ 4 super Yang-Mills theory. From these operators, we extract a spectrum of anomalous dimension up to six loops. We find that the spectrum agrees perfectly with the prediction based on quantum integrability. In evaluating the six-loop diagrams, we utilized a remarkable integer-relation algorithm developed
Anomalous generation of Chern-Simons terms in D=3, N=2 supersymmetric gauge theories
Letters in Mathematical Physics, 1986
Parity-invanant three-dimenstonal gauge theories with N = 2 extended supersymmetry are studied by the heat kernel method. The parity-anomalous part of the one-loop effective action is exactly found. It is expressed in terms of the N = 2 supersymmetric Chern-Simons term and is identified as a N = 2 superspace Atiyah-Patodi-Singer eta-invariant.
2017
In this paper, we show that tree level 2→ 2 scattering amplitudes in 3d N=2 Chern-Simons theory coupled to a fundamental chiral multiplet are dual superconformal invariant.We further show that the large N all loop exact amplitude computed in arXiv:1505.06571, also has dual superconformal symmetry, which implies dual superconformal symmetry is all loop exact which is in contrast to other known highly supersymmetric examples such as N=4 SYM and ABJM where the dual superconformal symmetry is in general anomalous. We then reverse the argument and ask, is it possible to fix the amplitude completely based on general principles. We show, dual superconformal invariance fixes the momentum dependent piece leaving the coupling constant dependence unfixed. We use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling constant dependence of scattering amplitude. We also show, in the dual space CFT, the four point scattering amplitude can be inte...