On the effective superpotential in the supersymmetric Chern-Simons theory with matter (original) (raw)

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.

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.

Superpotentials for superconformal Chern–Simons theories from representation theory

Journal of Physics A: Mathematical and Theoretical, 2009

These notes provide a detailed account of the universal structure of superpotentials defining a large class of superconformal Chern-Simons theories with matter, many of which appear as the low-energy descriptions of multiple M2-brane configurations. The amount of superconformal symmetry in the Chern-Simons-matter theory determines the minimum amount of global symmetry that the associated quartic superpotential must realise, which in turn restricts the matter superfield representations. Our analysis clarifies the necessary representationtheoretic data which guarantees a particular amount of superconformal symmetry. Thereby we shall recover all the examples of M2-brane effective field theories that have appeared in the recent literature. The results are based on a refinement of the unitary representation theory of Lie algebras to the case when the Lie algebra admits an ad-invariant inner product. The types of representation singled out by the superconformal symmetry turn out to be intimately associated with triple systems admitting embedding Lie (super)algebras and we obtain a number of new results about these triple systems which might be of independent interest. In particular, we prove that any metric 3-Lie algebra embeds into a real metric 3-graded Lie superalgebra in such a way that the 3-bracket is given by a nested Lie bracket.

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

Supersymmetric states in large N Chern-Simons-matter theories

Journal of High Energy Physics, 2012

In this paper we study the spectrum of BPS operators/states in N = 2 superconformal U (N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersymmetric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N = 2 theory with no superpotential, we study the renormalization of R-charge at finite 't Hooft coupling using "Z-minimization". A particularly intriguing result is found in the case of one adjoint matter. 6.4 Conjecture for the supersymmetric spectrum of the theory with a Tr Φ 3 superpotential 34 7. Supersymmetric states in the theory with two adjoint fields and vanishing superpotential 35 8. Supersymmetric states in the N = 3 theory with two adjoint chiral multiplets (i.e. one adjoint hypermultiplet) 36 8.1 Superconformal index 36 8.2 Supersymmetric cohomology 37 9. Marginal N = 2 deformations of the N = 3 theory 38 9.1 Superconformal index of these theories 40 9.2 Conjecture for the supersymmetric cohomology 40 9.3 Theories with three or more chiral multiplets 41 10. Superconformal index at finite k and N from localization 42 11. Discussion 44 Appendices 46 A. Details of numerics and plots 46 B. Cohomology calculation 51

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.

Two-loop low-energy effective action in Abelian supersymmetric Chern–Simons matter models

Nuclear Physics B, 2014

We compute two-loop low-energy effective actions in Abelian Chern-Simons matter models with N = 2 and N = 3 supersymmetry up to four-derivative order. Calculations are performed with a slowly-varying gauge superfield background. Though the gauge superfield propagator depends on the gauge fixing parameter, it is shown that the obtained results are independent of this parameter. In the massless case the considered models are superconformal. We demonstrate that the superconformal symmetry strongly restricts the form of two-loop quantum corrections to the effective actions such that the obtained terms have simpler structure than the analogous ones in the effective action of three-dimensional supersymmetric electrodynamics (SQED) with vanishing topological mass.

On Superspace Chern-Simons-like Terms

Journal of High Energy Physics, 2005

We search for superspace Chern-Simons-like higher-derivative terms in the low energy effective actions of supersymmetric theories in four dimensions. Superspace Chern-Simons-like terms are those gauge-invariant terms which cannot be written solely in terms of field strength superfields and covariant derivatives, but in which a gauge potential superfield appears explicitly. We find one class of such four-derivative terms with N = 2 supersymmetry which, though locally on the Coulomb branch can be written solely in terms of field strengths, globally cannot be. These terms are classified by certain Dolbeault cohomology classes on the moduli space. We include a discussion of other examples of terms in the effective action involving global obstructions on the Coulomb branch.

The quantum theory of Chern-Simons supergravity

Journal of High Energy Physics, 2019

We consider AdS 3 N-extended Chern-Simons supergravity (à la Achucarro-Townsend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gauge-fixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion.

ℵ0-extended supersymmetric Chern-Simons theory for arbitrary gauge groups

Physical Review D, 2004

We present a model of supersymmetric non-Abelian Chern-Simons theories in three-dimensions with arbitrarily many supersymmetries, called ℵ 0-extended supersymmetry. The number of supersymmetry N equals the dimensionality of any non-Abelian gauge group G as N = dim G. Due to the supersymmetry parameter in the adjoint representation of a local gauge group G, supersymmetry has to be local. The minimal coupling constant is to be quantized, when the homotopy mapping is nontrivial: π 3 (G) = Z Z. Our results indicate that there is still a lot of freedom to be explored for Chern-Simons type theories in three dimensions, possibly related to M-theory.