Renormalizations in supersymmetric and nonsupersymmetric non-abelian Chern-Simons field theories with matter (original) (raw)
Related papers
Supersymmetric non-Abelian non-commutative Chern–Simons theory
Physics Letters B, 2006
In this work, we study the three-dimensional non-Abelian noncommutative supersymmetric Chern-Simons model with the U (N ) gauge group. Using a superfield formulation, we prove that, for the pure gauge theory, the Green functions are one-loop finite in any gauge, if the gauge superpotential belongs to the fundamental representation of u(N ); this result also holds when matter in the fundamental representation is included. However, the cancellation of both ultraviolet and ultraviolet/infrared infrared divergences only happens in a special gauge if the coupling of the matter is in the adjoint representation. We also look into the finite one-loop quantum corrections to the effective action: in the pure gauge sector the Maxwell together with its corresponding gauge fixing action are generated; in the matter sector, the Chern-Simons term is generated, inducing a shift in the classical Chern-Simons coefficient. * Electronic address: alysson,mgomes,ajsilva@fma.if.usp.br † Electronic address: petrov@fisica.ufpb.br
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.
Four-fermion field theories and the Chern-Simons field: A renormalization group study
Physical Review D, 1999
In (2+1) dimensions, we consider the model of a N flavor, two-component fermionic field interacting through a Chern-Simons field besides a four fermion self-interaction which consists of a linear combination of the Gross-Neveu and Thirring like terms. The four fermion interaction is not perturbatively renormalizable and the model is taken as an effective field theory in the region of low momenta. Using Zimmerman procedure for reducing coupling constants, it is verified that, for small values of the Chern-Simons parameter, the origin is an infrared stable fixed point but changes to ultraviolet stable as α becomes bigger than a critical α c . Composite operators are also analyzed and it is shown that a specific four fermion interaction has an improved ultraviolet behavior as N increases. Fermionic quartic interactions have been very important for the clarification of conceptual aspects as well as for the applications of Quantum Field Theory. Illustrative examples of such dual role are provided by the Thirring and Nambu-Jona Lasinio models. However, perturbative studies of the models have been hampered by the fact that only in two dimensions they are renormalizable. If the number of flavors is high enough, a better ultraviolet behavior is achieved in the context of the 1/N expansion which turns out to be renormalizable up
Two-loop analysis of non-Abelian Chern-Simons theory
Physical Review D, 1992
Perturbative renormalization of a non-Abelian Chern-Simons gauge theory is examined. It is demonstrated by explicit calculation that, in the pure Chern-Simons theory, the beta-function for the coefficient of the Chern-Simons term vanishes to three loop order. Both dimensional regularization and regularization by introducing a conventional Yang-Mills component in the action are used. It is shown that dimensional regularization is not gauge invariant at two loops. A variant of this procedure, similar to regularization by dimensional reduction used in supersymmetric field theories is shown to obey the Slavnov-Taylor identity to two loops and gives no renormalization of the Chern-Simons term. Regularization with Yang-Mills term yields a finite integer-valued renormalization of the coefficient of the Chern-Simons term at one loop, and we conjecture no renormalization at higher order. We also examine the renormalization of Chern-Simons theory coupled to matter. We show that in the non-abelian case the Chern-Simons gauge field as well as the matter fields require infinite renormalization at two loops and therefore obtain nontrivial anomalous dimensions. We show that the beta function for the gauge coupling constant is zero to two-loop order, consistent with the topological quantization condition for this constant.
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...
Renormalization group improvement of the superpotential for the N = 2 Chern-Simons-matter model
Renormalization group improvement of the superpotential for the N = 2 Chern-Simons-matter model, 2020
Within the superfield formalism, we study the renormalization group improvement of the effective superpotential for the N ¼ 2 Chern-Simons-matter theory, explicitly obtain the improved effective potential and discuss the minima of the effective potential and a problem of mass generation in the theory.
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
Arxiv preprint arXiv:1106.5144, 2011
Recent studies of the AdS 4 /CF T 3 correspondence involve the construction of a peculiar supersymmetric gauge theory on the worldvolume of multiple M2s branes as a boundary field theory. Under suitable conditions the quantum theory becomes a noncommutative supersymmetric YM-CS gauge theory which call for an study of its renormalized perturbative corrections. As a preliminary step to more general consideration, the modification of the N = 3, 2, 1 supersymmetric YM-CS gauge theory due to noncommutativity of spatial coordinates is proposed. We carry out the one-loop renormalization and a noncommutative correction for the Chern-Simons coefficient is obtained. Finally it is found that this new correction depends of the noncommutative parameter in an analytic form.
Supersymmetric Chern-Simons theories with vector matter
Journal of High Energy Physics, 2012
In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N = 2 supersymmetric model (with one chiral field) for all values of the 't Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.