Superfield Techniques Research Articles

SU(2|2) supersymmetric mechanics

We introduce a new kind of non-relativistic ${\cal N}{=}\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\cal N}{=}\,8$, $d{=}1$ supersymmetry. Various worldline $SU(2|2)$ superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell $SU(2|2)$ multiplets $({\bf 3,8,5})$, $({\bf 4,8,4})$ and $({\bf 5,8,3})$, we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group $OSp(4^*|4)$ in the conformal cases. For the simplest $({\bf 5, 8, 3})$ model the quantization is performed.

Multimetric supergravities

Making use of integral forms and superfield techniques we propose supersymmetric extensions of the multimetric gravity Lagrangians in dimensions one, two, three and four. The supersymmetric interaction potential covariantly deforms the bosonic one, producing in particular suitable super-symmetric polynomials generated by the Berezinian. As an additional application of our formalism we construct supersymmetric multi-Maxwell theories in dimensions three and four.

Lorentz-violating quantum electrodynamics in two-dimensional aether-superspace

The two-dimensional aether-superspace is constructed and the superfield techniques are applied to the study of the dynamical generation of mass in the Lorentz-violating supersymmetric quantum electrodynamics in two dimensions of spacetime. It is shown that such model presents a dynamical generation of mass for the gauge aether-superfield and its dispersion relation has a structure similar to that of the CPT-even Lorentz-breaking models.

The one-loop effective potential of the Wess-Zumino model revisited

The full one-loop supersymmetric effective potential for the Wess-Zumino model is calculated using superfield techniques. This includes the K\"ahler potential and the auxiliary field potential, of which the former was originally computed in 1993 while the latter is derived for the first time. In the purely bosonic sector our results match those of older component field calculations. In light of prior contradictory results found in the literature, the calculation of the leading term in the auxiliary field potential is approached in a variety of ways. Issues related to conditional convergence that occur during these calculations and their possible consequences are discussed.

Two-loop effective potential for the Wess-Zumino model in2+1dimensions

By using superfield techniques, the effective potential of the $\mathcal{N}=1$ Wess-Zumino model in 2+1 dimensions is computed off-shell up to two loops. It is shown that supersymmetry is not dynamically broken, and that dynamical generation of mass does not occur perturbatively. We also investigate the renormalization of the effective potential and determine the renormalization group gamma and beta functions, showing that this model is infrared free. Comparison with some other results in the literature is provided.

An Elementary Proof of the Non-Renormalization Theorem for the Wess-Zumino Model

Using the exact renormalization group (ERG) differential equation, we give an elementary proof of the non-renormalization theorem for the Wess-Zumino model. We introduce auxiliary fields to linearize the supersymmetry transformation, but we do not rely on the superfield techniques. We give sufficient background material on the Wilson action and the ERG formalism to make the paper self-contained.

6D supersymmetric nonlinear sigma-models in 4D, Script N = 1 superspace

Using 4D, N=1 superfield techniques, a discussion of the 6D sigma-model possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a doublet of chiral scalar superfields for each 6D hypermultiplet. A second description that is most directly related to projective superspace is also presented. The latter necessarily implies the use of one chiral superfield and one nonminimal scalar superfield for each 6D hypermultiplet. A separate study of models of this class, outside the context of projective superspace, is also undertaken.

Formula omitted] supersymmetric planar particles and magnetic interaction from noncommutativity

We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N=2 superfield technique and show that in the presence of a scalar N=2 superpotential the magnetic interaction is implied by the presence of noncommutativity of position variables. Further, by expressing the supersymmetric Hamiltonian as a bilinear in N=2 supercharges we obtain two supersymmetric models with electromagnetic interactions and two different noncanonical simplectic structures describing noncommutativity. We show that both models are related to each other by a noncanonical transformation of phase space variables supplemented by a Seiberg–Witten map of the gauge potentials.

Coupling of fermions to the three-dimensional noncommutativeCPN−1model: Minimal and supersymmetric extensions

We consider the coupling of fermions to the three-dimensional noncommutative ${\mathrm{CP}}^{N\ensuremath{-}1}$ model. In the case of minimal coupling, although the infrared behavior of the gauge sector is improved, there are dangerous (quadratic) infrared divergences in the corrections to the two-point vertex function of the scalar field. However, using superfield techniques we prove that the supersymmetric version of this model with ``antisymmetrized'' coupling of the Lagrange multiplier field is renormalizable up to the first order in $1/N.$ The auxiliary spinor gauge field acquires a nontrivial (nonlocal) dynamics with generation of Maxwell and Chern-Simons noncommutative terms in the effective action. Up to $1/N$ order all divergences are only logarithmic so that the model is free from nonintegrable infrared singularities.

Goldstone superfield actions in AdS5 backgrounds

Nonlinear realizations superfield techniques, pertinent to the description of partial breaking of global N=2 supersymmetry in a flat d=4 super-Minkowski background, are generalized to the case of partially broken N=1 AdS 5 supersymmetry SU(2,2|1). We present, in an explicit form, off-shell manifestly N=1, d=4 supersymmetric minimal Goldstone superfield actions for two patterns of partial breaking of SU(2,2|1) supersymmetry. They correspond to two different nonlinear realizations of the latter, in the supercosets with the AdS 5 and AdS 5× S 1 bosonic parts. The relevant worldvolume Goldstone supermultiplets are accommodated, respectively, by improved tensor and chiral N=1, d=4 superfields. The second action is obtained from the first one by dualizing the improved tensor Goldstone multiplet into a chiral Goldstone one. In the bosonic sectors, the first and second actions yield static-gauge Nambu–Goto actions for a L3-brane on AdS 5 and a scalar 3-brane on AdS 5× S 1.

Basic and equivariant cohomology in balanced topological field theory

We present a detailed algebraic study of the N=2 cohomological set-up describing the balanced topological field theory of Dijkgraaf and Moore. We emphasize the role of N=2 topological supersymmetry and sl(2, R) internal symmetry by a systematic use of superfield techniques and of an sl(2, R) covariant formalism. We provide a definition of N=2 basic and equivariant cohomology, generalizing Dijkgraaf’s and Moore’s, and of N=2 connection. For a general manifold with a group action, we show that: (i) the N=2 basic cohomology is isomorphic to the tensor product of the ordinary N=1 basic cohomology and a universal sl(2, R) group theoretic factor; (ii) the affine spaces of N=2 and N=1 connections are isomorphic.

Osp(|4) supermultiplets as conformal superfields on AdS4 and the generic form of = 2, d = 3 gauge theories

In this paper we fill a necessary gap in order to realize an explicit comparison between the Kaluza-Klein spectra of supergravity compactified on AdS4 × X 7 and superconformal field theories living on the worldvolume of M2-branes. On the algebraic side we consider the superalgebra Osp(| 4) and we study the double interpretation of its unitary irreducible representations either as supermultiplets of particle states in the bulk or as a conformal superfield on the boundary. On the Lagrangian field theory side we construct, using rheonomy rather than superfield techniques, the generic form of an = 2, d = 3 gauge theory. Indeed, the superconformal multiplets are supposed to be composite operators in a suitable gauge theory.

A new class of superconformal sigma models with the Wess-Zumino action

We construct nonlinear sigma models for infinite-dimensional N-extended D = 2 superconformal symmetries (of the type ( N, N)). These are classically integrable and naturally incorporate the conformally invariant bosonic Wess-Zumino sigma model defined on the supersymmetry automorphism group SO −( N) × SO +( N). Their bosonic manifolds involve also the D = 2 dilaton and, in general, a number of additional fields. For the dilaton, both the free and Liouville actions are admissible (in the latter case - supplemented with proper Yukawa couplings), so the proposed models simultaneously provide higher- N superextensions of the D = 2 Liouville theory. Manifestly invariant superfield techniques are employed. A finite set of basic Nambu-Goldstone superfields is singled out by imposing infinitely many covariant constraints on the relevant Cartan 1-forms. The resulting superfield equations of motion and off-shell irreducibility conditions have a universal form for any N. We solve the irreducibility conditions on-shell for arbitrary N and off-shell for N ⩽ 4. The N = 3 and N = 4 models are examined in detail. These are the first examples of self-contained lagrangian models respecting superconformal symmetry with non- canonical generators (spontaneously broken). A generalization to the heterotic case and possible implications in the string theory are briefly outlined.

Enhancement factors for supersymmetric proton decay in SU(5) and SO(10) with superfield techniques

The anomalous dimensions of the proton decay operators of dimension six are calculated in supersymmetric SU(5) and SO(10) with superfield techniques. The corresponding enhancement factors are remarkably similar in both cases and practically identical to the non-supersymmetric case. Also results are given for the enhancement factors of the dimension-five operators for both unification groups.

A simple implementation of Wess-Zumino-like gauges within the superfield technique

Within the context of the superfield formalism we present a class of Wess-Zumino-like gauges induced by a simple non-supersymmetric gauge fixing term, thus eliminating the spurious infrared singularity of the vector-superfield propagator without abandoning the efficiency of supergraph techniques.

Representations of low-rank orthosymplectic superalgebras by superfield techniques

Representations of Lie superalgebras may be realised as functions (superfields) on graded manifolds (suitably chosen onset spaces). The technique is illustrated for OSp(1/2) and OSp(2/2) with a review of well known results, and applied in the cases of OSp(3/2) and OSp(4/2) to construct some classes of irreducible representations.

Superloops 3, beta 0: A calculation in N = 4 Yang-Mills theory

We present details of a calculation using superfield techniques, to show that the β-function is zero to 3 loops in N = 4 supersymmetric Yang-Mills theory.

Diagram and superfield techniques in the classical superalgebras

Introduces the concept of 'graded permutation group' in the analysis of tensor operators in the classical superalgebras. For U(m/n) and SU(m/n), irreducible tensor representations correspond to classes of Young tableaux with definite graded symmetry type. Diagram techniques are given for Kronecker products, dimensions, and branching rules. The tensor techniques are complemented by the introduction of a superfluid formalism, in which U(m/n) and SU(m/n) act on (polynomial) functions over the appropriate superspace. Such superfluids may admit constraints. A general superfield interpolates between the classes of Young tableaux which correspond to particular types of constraint. The tensor and superfield techniques are illustrated with case studies of SU(2/1) and SU(m/1).

Superspace action for a 6-dimensional non-extended supersymmetric Yang-Mills theory

The ordinary N = 2 extended (abelian) gauge theory is written in the framework of a non-extended theory in 6-dimensional superspace. Graded differential geometry and superfield technique is used to construct a superspace action. The x-space lagrangian arises as the term of second order in θ of the superspace lagrangian.

Zero Value for the Three-LoopβFunction inN=4Supersymmetric Yang-Mills Theory

This Letter describes a calculation using superfield techniques, showing that the $\ensuremath{\beta}$ function is zero to three loops in $N=4$ supersymmetric Yang-Mills theory. This result gives further indication that the theory is likely to be finite and conformally invariant order by order in perturbation theory.