Anomalous generation of Chern-Simons terms in D=3, N=2 supersymmetric gauge theories (original) (raw)

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.

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

Generalized Chern-Simons Terms and Chiral Anomalies in N=1 Supersymmetry

2008

The gauging of axionic, Stueckelberg-type, shift symmetries with generalized Chern-Simons terms and the Green-Schwarz mechanism of anomaly cancellation has recently been studied in the context of certain string compactifications and with regard to the phenomenology of unusual variants of Z'-bosons. In this talk, following recent work with De Rydt, Rosseel, Schmidt and Van Proeyen, I summarize how such theories can be reconciled with global and local N=1 supersymmetry. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups.

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.

N = 1 super-Chern-Simons coupled to parity-preserving matter from Atiyah-Ward space-time

Physics Letters B, 1996

In this letter, we present the Parkes-Siegel formulation for the massive Abelian N =1 super-QED 2+2 coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from (2+2) to (1+2) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the τ 3 QED 1+2 coupled to a Chern-Simons term naturally comes out.

Dual superconformal symmetry of N=6 Chern-Simons theory

2010

ABSTRACT We demonstrate that the four and six-point tree-level amplitudes of N = 6 \mathcal{N} = 6 superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some implications of dual conformal symmetry for loop-level amplitudes. KeywordsChern-Simons Theories-Superspaces-AdS-CFT Correspondence-Integrable Field Theories

Self-duality of three-dimensional Chern-Simons theory

Nuclear Physics B, 1991

We describe a precise self-duality relation between the electric charge and magneüc flux vortex sectors in the (2 + 1)-dimensional 71N gauge Higgs model with Chern-Simons term. The phase structure of this model is deduced using the self-duality . In particular, we find that the Chern-Simons term suppresses the confinement phase. Compact U(1) pure Chern-Simons theory corresponds to an N~x, infinite bare gauge coupling and zero bare mass limit. The self-duality of Chern-Simons theory is used to explain the hierarchy of odd-denominator filling fractions in the fractional quantum Hall effect and to seggest similar hierarchical ground-state structures in theories of the anyon and high-temperature superconductivity. Possible extensions to the nonabelian gauge groups and connection to the two-dimensional conformal field theories are also discussed .

Chern-Simons coefficient in supersymmetric non-Abelian Chern-Simons Higgs theories

Physical Review D, 1999

By taking into account the effect of the would be Chern-Simons term, we calculate the quantum correction to the Chern-Simons coefficient in supersymmetric Chern-Simons Higgs theories with matter fields in the fundamental representation of SU (n). Because of supersymmetry, the corrections in the symmetric and Higgs phases are identical. In particular, the correction is vanishing for N = 3 supersymmetric Chern-Simons Higgs theories. The result should be quite general, and have important implication for the more interesting case when the Higgs is in the adjoint representation.

The Integral Form of D = 3 Chern-Simons Theories Probing Cn/Γ Singularities

Fortschritte der Physik, 2017

We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS 4 /CFT 3 correspondence. From the structural viewpoint , we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kähler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS 4 /CFT 3 correspondence and more generally of M2-branes we emphasize the role of the Kähler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non-compact Kähler quotient K 4 of some flat variety with respect to a suitable group. The crepant resolutions of C n /Γ singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern-Simons Theory supposedly dual to the corresponding M2-brane solution.