Wess-Zumino Gauge Research Articles

Chiral anomalies and supersymmetry

The structure of the chiral anomalies in supersymmetric gauge theories is studied. We discuss in detail the relationship between the two pictures: the manifestly SUSY-covariant approach and the Wess-Zumino gauge. A prescription for the computation of the anomalies in higher dimensions is presented and the resulting expression in six dimensions is reported.

Supersymmetry anomally in two dimensions

In two dimensions we obtain a supersymmetric extension of a gauge anomaly, and find that this is the origin of a supersymmetry anomaly in the Wess-Zumino gauge. We also obtain an effective action whose variations give rise to the gauge and supersymmetry anomalies.

Instantons and the renormalisation group in supersymmetric Yang-Mills theories

The renormalisation group requires that in supersymmetric Yang-Mills theories the one- and two-loop quantum corrections to the vacuum energy (and related quantities) in an instanton background field vanish, at least for the terms proportional to In μ, where μ is the renormalisation point. It has recently been suggested that this result can be generalised to all orders in perturbation theory. We verify the two-loop calculation result by explicit calculation, both in the Wess-Zumino gauge and using covariant supergraphs. This requires a careful treatment of both the bosonic and fermionic (including the supergauge) zero modes. The subtleties and compliccations of our calculation and the cancellation mechanism make it difficult to imagine howa general all-orders argument might be constructed.

Supersymmetry anomalies and some aspects of renormalization

Hiroshi ITOYAMA Physics Department, Columbia University, New York, NY 10027, USA V.P. NAIR and Hai-cang REN Institute for Advanced Study, Princeton, NJ 08540, USA Received 1 May 1985 We show how the 5e-matrix elements avoid the problem of supersymmetry breaking by the gauge fixing and ghost terms for renormalization in the Wess-Zumino gauge. Possible origins of supersymmetry anomalies are discussed. Gauge and gravitational anomalies induce a supersym- metry anomaly which has two distinct terms, one of which is gauge invariant. We give the expression for the noninvariant term for 2n-dimensional spacetime and for the invariant part in four dimensions. This anomaly, although cohomologically nontrivial, is still consistent with the result that in superspace no supersymmetry anomaly is generated.

Comment on the nonrenormalization theorem in supersymmetric gauge theories

We discuss some subtleties connected with the nonrenormalization theorem in supersymmetric gauge theories. In particular, we reconcile the need for infinite-mass counterterms in the Wess-Zumino gauge with the existence of the theorem.

Enhancement factors for supersymmetric proton decay in the Wess-Zumino gauge

We calculate the anomalous dimensions of the proton decay operators of dimensions 5 and 6 in supersymmetric SU(5). We perform the calculations in a general covariant Wess-Zumino gauge in which the computations lead to the simultaneous renormalization of a set of component operators which mix among themselves and hence do not have definite anomalous dimensions. The particular combinations of component operators contained in (superfield) supersymmetric operators have definite anomalous dimensions. We find that the enhancement factors for the dimension-6 operators in the supersymmetric case are practically identical to the corresponding non-supersymmetric enhancement factors.

From N = 1 to N = 4 extended supersymmetric Yang-Mills fields in a covariant Wess-Zumino gauge

It is assumed that N = 1 supersymmetric Yang-Mills fields coupled to chiral matter fields can be renormalized in a covariant Wess-Zumino gauge with a minimal number of subtractions so that the Ward identities of supersymmetry, ordinary gauge invariance and matter-field-flavour symmetries are satisfied. The chiral Yukawa couplings are supposed to remain unrenormalized. I show that on the basis of these assumptions an N = 4 extended manifestly O(4) invariant theory can be constructed with finite Yukawa and φ 4 couplings. A consequence of these non-renormalizations is the vanishing of the renormalization group β function.

Auxiliary field-free supersymmetric gauges

We find that, in perturbation theory, non-light-cone axial gauges, N ∘ A a ( x) = 0, preserve the supersymmetry remaining in N = 1 supersymmetric YM theories, after imposing the Wess-Zumino gauge.

Multiplicative renormalizability of Abelian supergauge theory in the Wess-Zumino gauge

It is shown that in the general case the renormalization of the Abelian supergauge supersymmetrical theory is not multiplicative. However, the renormalization is multiplicative in the supersymmetrical gauge and the Wess-Zumino gauge.

Renormalizability of an Abelian supergauge theory in the Wess-Zumino gauge

The renormalization of an Abelian supergauge supersymmetry theory in the class of gauges including the supersymmetry gauge and the Wess-Zumino gauge conserves the symmetry properties of the theory.

Supersymmetric regulators and supercurrent anomalies

The supercurrent anomalies of the supercurrent S μ of the supersymmetric Yang-Mills theory in Wess-Zumino gauge are computed using the supersymmetric dimensional regulator of Siegel. It is shown that γ μ S μ=0 and ∂ μ S μ≠0 in agreement with an earlier calculation based on the Adler-Rosenberg method. The problem of exhibiting the chiral anomaly and a regulator for local supersymmetry suggests that the interpretation of dimensional reduction in component language is incomplete.

Supersymmetry Ward identity for the supersymmetric non-Abelian gauge theory

It is shown by direct computation that the supersymmetry Ward identity for the supersymmetric Yang-Mills theory can be satisfied at the one-loop level in the Wess-Zumino gauge when one uses dimensional regularization with the prescription ${\ensuremath{\gamma}}^{\ensuremath{\mu}}{\ensuremath{\gamma}}_{\ensuremath{\mu}}=4$, and performs the Dirac algebra in four dimensions. The result is found to be valid for arbitrary covariant gauge-fixing functionals. A particular gauge, $\ensuremath{\xi}=\ensuremath{-}3$, is found for which the supersymmetry transformations of both renormalized and unrenormalized fields are finite and well defined. In this same gauge, one-loop renormalization constants for two-, three-, and four-point one-particle-irreducible Green's functions are found to be equal.

On the auxiliary fields of supergravity

The relation between two sets of auxiliary fields for supergravity, i.e. the Lie algebra valued vector multiplet in the Wess-Zumino gauge and the minimal set with 6 auxiliary fields is exhibited. This gives rise to a formulation with a gauge multiplet for the chiral transformations.

Higgs model and supersymmetry

The Higgs model can be made supersymmetric, provided a Dirac spinor is added, and the quartic interaction term in the Lagrangian density is —(e2/2)(ϕ†φ)2, wheree is the gauge coupling constant. The model describes a vector, a Dirac spinor and a real scalar; it depends only on two arbitrary parameters,m ande. As a gauge-invariant model, it can be studied in a Wess-Zumino gauge, or in a supersymmetric gauge. It can also be obtained as a theory of a self-interacting vector multiplet. Finally, it is suggested that a scalar particle may be associated with the photon and the two neutrinos in the theory of weak and electromagnetic interactions.

Combined supersymmetric and gauge-invariant field theories

The combined supersymmetric and gauge-invariant field theories are formulated using ordinary fields, not superfields, from the start, thereby eliminating reference to superfluous components. The construction is a generalization to supersymmetry of the minimal-coupling procedure of ordinary gauge theories. The Lagrangians obtained coincide with those of the superfield approach in the Wess-Zumino gauge. The Ward-Takahashi identities of Green's functions for fields and supersymmetry currents are obtained by functional methods. The Ward-Takahashi identities are presented in a form from which low-energy theorems for Goldstone fermions can be directly derived, and the proof of the Goldstone theorem in these combined theories is clarified. Discussion of the closure of the supersymmetry algebra leads to the concept of gauge-invariant translations for which the conserved current is a gravitational energy-momentum tensor. Some of the results are valid in a broader context than supersymmetry and are applicable to gauge theories in general.