Supergauge Invariance Research Articles

Covariant quantization of N=1/2 SYM theories and supergauge invariance

So far, quantum properties of N=1/2 nonanticommutative (NAC) super Yang--Mills theories have been investigated in the WZ gauge. The gauge independence of the results requires assuming that at the quantum level supergauge invariance is not broken by nonanticommutative geometry. In this paper we use an alternative approach which allows studying these theories in a manifestly gauge independent superspace setup. This is accomplished by generalizing the background field method to the NAC case, by moving to a momentum superspace where star products are treated as exponential factors and by developing momentum supergraph techniques. We compute the one--loop gauge effective action for NAC U(N) gauge theories with matter in the adjoint representation. Despite the appearance of divergent contributions which break (super)gauge invariance, we prove that the effective action at this order is indeed invariant.

GAUGE-INVARIANT REGULARISATION VIA SU(N|N)

We construct a gauge-invariant regularisation scheme for pure SU(N) Yang–Mills theory in dimension four or less (for N = ∞ in all dimensions), with a physical cutoff scale Λ, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing their powers are within certain ranges, the covariant higher derivatives cure the superficial divergence of all but a set of one-loop graphs. The finiteness of these latter graphs is ensured by properties of the supergroup and gauge invariance. In the limit Λ → ∞, all the regulator fields decouple and unitarity is recovered in the renormalized pure SU(N) Yang–Mills theory. By demonstrating these properties, we prove that the regularisation works to all orders in perturbation theory.

A note on the effective soft SUSY-breaking Lagrangian below the GUT scale

I consider the superfield derivation of the effective theory of softly broken supersymmetry below the GUT scale. I point out the role of supergauge invariance in determining the form of the result, which is rather restricted in interesting classes of models. As an example I discuss sfermion mass splittings for matter embedded in a single GUT multiplet. Interesting differences arise between the cases of SU(5), SO(10) and E 6.

Restricted supergauge invariance, N = 2 coadjoint orbits and N = 2 quantum supergravity

It is shown that the N = 2 superconformal transformations are restricted N = 1 supergauge transformations of a supergauge theory with Osp(2, 2) as a gauge group. Based on this result, a canonical derivation of the Osp(2, 2) current algebra in the superchiral gauge formulation of N = 2 supergravity is presented.

Supergauge invariant Lagrangians from Noether identities

Starting from the supergauge invariance suggested by physical requirements, the authors set up the corresponding Noether identities and determine the most general Lagrangian which satisfies them.

Path integral quantization of the supersymmetric model of the Dirac particle

We investigate in detail the representation of the Dirac propagator as a path integral over virtual trajectories in the phase space with anticommuting variables. Using the reparametrization and supergauge invariant action integral proposed by Berezin and Marinov [Ann. Phys. 104, 336 (1977)], we analyze the relation of causality to reparametrization invariance, and we construct the Faddeev–Popov measure for the symbol of the evolution operator. We present a precise definition of the path integral as a limit of finite-dimensional integrals, and we explicitly perform the integration obtaining the familiar result. We also analyze another approach, where reparametrization and supergauge invariance of the action is preserved with the help of independent einbein variables. This method, as opposed to Faddeev–Popov technique, dispenses with the gauge fixing problem and allows us to construct the correct functional measure by explicit factorization of the volume of reparametrization group and supergauge group; the former is infinite, the latter identically vanishes. A sequence of finite-dimensional approximations to the functional measure is given also in this case together with explicit calculations.

Local supersymmetry in superspace

Supersymmetric Yang-Mills and gravitational theories are formulated in terms of connections on superspace. The anticommutator of the spinor components of the connections are constrained. This gives the usual supersymmetric Yang-Mills theory and a formulation of supergravity in terms of a gauge phase factor. Supergauge invariance is used to reduce the phase factor to Wess-Zumino form, leaving the local supersymmetry algebra which agrees with the transformations of Breitenlohner.

Geometrical approach to local gauge and supergauge invariance: Local gauge theories and supersymmetric strings

Geometrical approach to local gauge and supergauge invariance: Local gauge theories and supersymmetric strings

Supergauge invariant extension of the Higgs mechanism and a model for the electron and its neutrino

We extend the Higgs mechanism in a supergauge invariant way. Spontaneous symmetry breaking occurs for all allowed values of the parameters of the scalar potential. With SU(2) × U(1) as gauge group and after spontaneous breaking of supergauge invariance, we obtain a model of weak and electromagnetic interactions for the electron and its neutrino, which includes also heavy leptons and scalar particles. The neutrino is the Goldstone fermion, associated with the photon in a massless vector multiplet.

Supergauge invariant Yang-Mills theories

We construct Lagrangian theories which are simultaneously invariant under supergauge transformations and under Yang-Mills transformations. The simplest of these turns out to be just the usual theory describing the interaction of a Yang-Mills field with a Majorana spinor belonging to the regular representation of the internal symmetry group. This theory is asymptotically free. Other examples, involving in addition to spinors also scalar and pseudoscalar fields are described. They also are asymptotically free, provided the number of scalar supermultiplets is not too high and supergauge invariance, as expected, is preserved by renormalization.

Spontaneously broken supergauge symmetries and goldstone spinors

We present a model with a spontaneously broken supergauge symmetry which results in the appearance of a massless Goldstone spinor. The model combines supergauge invariance with ordinary gauge invariance. After the breaking the gauge boson acquires a mass as a result of the Higgs mechanism.

Broken supergauge symmetry and renormalization

A field theory model invariant under supergauge transformations is shown to be renormalizable to all orders in perturbation theory. Renormalization is shown to be consistent with supergauge invariance. It is further shown that only one renormalization constant is needed, a common wave function renormalization for all fields. A symmetry breaking term iis introduced which breaks the symmetry explicitly but so smoothly that the renormalization procedure of the symmetric case can still be applied. Relations among masses and coupling constants emerge. Among other topics discussed, the possibility that the supergauge symmetry is spontaneously broken and that a Goldstone spinor appears is examined.

A lagrangian model invariant under supergauge transformations

We study, in the one-loop approximation, a Lagrangian model invariant under supergauge transformations. The model involves a scalar, a pseudoscalar and a spinor field. Supergauge invariance gives rise to relations among the masses and the coupling of these fields and implies the existence of a conserved current. The renormalization procedure is discussed and the relations among masses and couplings are shown to be preserved by renormalization.