Renormalization and symmetry conditions in supersymmetric QED

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov–Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms. Received: 23 July 1999 / Published online: 14 October 1999     

Supersymmetry and singular potentials

The breaking of supersymmetry due to singular potentials in supersymmetric quantum mechanics is critically analyzed. It is shown that, when properly regularized, these potentials respect supersymmetry, even when the regularization parameter is removed.     

Regularizations and superconformal anomalies

By using different regularization methods we demonstrate that supersymmetry invariance is maintained up to one-loop order in supersymmetric gauge theories and calculate the superconformal anomalies.     

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories

We apply the technique of dimensional reduction to both supersymmetric and non-supersymmetric theories. Explicit one- and two-loop calculations show that in the latter case the technique is a viable alternative to conventional dimensional regularization, while in the former it preserves the Slavnov-Taylor identities of both supersymmetry and gauge invariance.     

Vacuum fluctuations of the supersymmetric field in curved background

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.     

Regularization and supersymmetry-restoring counterterms in supersymmetric QCD

We calculate symmetry-restoring counterterms in supersymmetric QCD at the one-loop level. First we determine loop corrections to the supersymmetry and gauge transformations and find counterterms in such a way that the symmetry algebra holds at the one-loop level. Then these results are used to derive the symmetry-restoring counterterms to all trilinear interactions. In order to obtain unique results it is crucial to use the Slavnov-Taylor identity, which does not only contain supersymmetric and gauge Ward identities but also describes the symmetry algebra. In dimensional regularization this procedure yields unique non-zero values for the counterterms. In contrast, in dimensional reduction we find that no non-symmetric counterterms are needed, neither for the symmetry transformations nor for the physical interactions. For the considered cases this result constitutes a definite test of the supersymmetry and gauge invariance of the scheme. Received: 1 March 2001 / Published online: 25 April 2001     

Noninvariance of regularization by dimensional reduction: An explicit example of supersymmetry breaking

By a direct calculation it is shown that at the three-loop level the regularization by dimensional reduction of Avdeev, Chochia and Vladimirov breaks supersymmetry relations between couplings in the N = 1, 2, 4 supersymmetric Yang-Mills theories written in terms of component fields. This is a strong limitation to the scope of the regularization.     

Supercurrent anomaly in non-abelian supersymmetric theories

A method for regularizing the supercurrent, preserving both gauge invariance and supersymmetry is developed, using point-splitting regularization and path-dependent phase factors in superspace. The supercurrent anomaly for general non-abelian supersymmetric theories is obtained on the mass-shell in the one-loop approximation.     

Semiclassical solutions ofOSp(N,4) supersymmetry 0

This work analyzes the connection between the so-called reflective boundary conditions and the spontaneous breaking of supersymmetry in anti-de Sitter background space. The one-loop effective potential of the Wess-Zumino model is computed using the supersymmetry invariant Pauli-Villars regularization procedure. The effect of the background geometry is determined exactly. It is shown that supersymmetry is preserved to the one-loop order at each classically supersymmetric extremum of the effective potential. Depending on the reflective boundary conditions chosen, quantum shifts in theA-field andB-field vacuum solutions are exhibited.     

Supersymmetric quantum hall liquid with a deformed supersymmetry

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore—Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudopotential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudopotential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.     

Supersymmetric quantum mechanics in one,two and three dimensions

We discuss a few supersymmetric quantum mechanical models in one, two and three dimensions. In the case of one particle in both two and three dimensions we present some examples where supersymmetry is unbroken and the ground state is many-fold degenerate. Further, we consider the supersymmetric generalization of the nearest neighbour XY model and show that supersymmetry remains unbroken in this case.     

Two-loop QCD amplitude for gg-->h, H in the minimal supersymmetric standard model

We present the two-loop QCD amplitude for the interaction of two gluons and a CP-even Higgs boson in the minimal supersymmetric standard model (MSSM). We apply a novel numerical method for the evaluation of Feynman diagrams with infrared, ultraviolet, and threshold singularities. We discuss subtleties in the ultraviolet renormalization of the amplitude with conventional dimensional regularization, dimensional reduction, and the four dimensional helicity scheme. Finally, we show numerical results for scenarios of supersymmetry breaking with a rather challenging phenomenology in which the Higgs signal in the MSSM is suppressed in comparison to the standard model.     

Search for supersymmetry at LHC

One of the main motivations for the experiments at the Large Hadron Collider (LHC), scheduled to start around 2006, is to search for supersymmetric particles. The region of the parameter space of the minimal supersymmetric standard model, where supersymmetry can be discovered, is investigated. We show that if supersymmetry exists at the electroweak scale, it would be easy to find signals for it at the LHC. If the LHC does find supersymmetry, this would be one of the greatest achievements in the history of theoretical physics.     

Finite-temperature supersymmetry: the Wess-Zumino model

We investigate the breakdown of supersymmetry at finite temperature. While it has been proven that temperature always breaks supersymmetry, the nature of this breaking is less clear. On the one hand, a study of the Ward-Takahashi identities suggests a spontaneous breakdown of supersymmetry without the existence of a Goldstino, while on the other hand it has been shown that in any supersymmetric plasma there should exist a massless fermionic collective excitation, the phonino. Aim of this work is to unify these two approaches. For the Wess-Zumino model, it is shown that the phonino exists and contributes to the supersymmetric Ward-Takahashi identities in the right way displaying that supersymmetry is broken spontaneously with the phonino as the Goldstone fermion.     

Supersymmetry and the anomalous anomalous magnetic moment of the muon

The recently reported measurement of the muon's anomalous magnetic moment differs from the standard model prediction by 2.6 sigma. We examine the implications of this discrepancy for supersymmetry. Deviations of the reported magnitude are generic in supersymmetric theories. Based on the new result, we derive model-independent upper bounds on the masses of observable supersymmetric particles. We also examine several model frameworks. The sign of the reported deviation is as predicted in many simple models, but disfavors anomaly-mediated supersymmetry breaking.     

A geometric formulation of supersymmetry

The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example, we introduce modified supersymmetry variations and redefined auxiliary fields that transform covariantly under reparametrizations. The resulting action and transformation laws are manifestly covariant and highlight the geometric structure of the supersymmetric theory. The covariant methods are developed first for general theories (not necessarily supersymmetric) whose scalar fields are coordinates of a Riemannian target space.     

Towards Higher-N Superextensions of Born–Infeld Theory

We give a brief account of supersymmetric Born–Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N = 3 supersymmetric Born–Infeld theory which admits a natural off-shell formulation in N = 3 harmonic superspace.     

Can supersymmetric theories be bosonized?

We investigate the possibility of transforming supersymmetric theories into pure;y fermionic or bosonic forms. The supersymmetric sine-Gordon lagrangian is rewritten in a purely fermionic form, and the Fermi equivalent of the original supersymmetry transformation is derived. This transformation represents an invariance only at the quantum level, when the effects of the chiral anomaly have been taken into account. When supersymmetric theories are written in purely bosonic forms, a non-local bosonic transformation takes place of the supersymmetry transformation. In both cases the supersymmetry algebra, as realized on the fields, is lost.     

The (2+1)-dimensional supersymmetric CPN−1 model and the central charge

The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CP^N?1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CP^N?1 model thus obtained admits an O(2) extended supersymmetry.