We show that top-quark pairs are produced in an essentially unique spin configuration in polarized e + e − colliders at all energies above the threshold region. Since the directions of the electroweak decay products of polarized top-quarks are strongly correlated to the top-quark spin axis, this unique spin configuration leads to a distinctive topology for top-quark pair events which can be used to constrain anomalous couplings to the top-quark. A significant interference effect between the longitudinal and transverse W-bosons in the decay of polarized top-quarks is also discussed. These results are obtained at leading order in perturbation theory but radiative corrections are expected to be small.

We study the non-perturbative behavior of some N = 1 supersymmetric product-group gauge theories with the help of duality. As a test case we investigate an SU(2) × SU(2) theory in detail. Various dual theories are constructed using known simple-group duality for one group or both groups in succession. Several stringent tests show that the low-energy behavior of the dual theories agrees with that of the electric theory. When the theory is in the confining phase we calculate the exact superpotential. Our results strongly suggest that, in general, dual theories for product groups can be constructed in this manner, by using simplegroup duality for both groups. Turning to a class of theories with SU(N) × SU(M) gauge symmetry we study the renormalization group flows in the space of the two gauge couplings and show that they are consistent with the absence of phase transitions. Finally, we show that a subset of these theories, with SU(N) × SU(N − 1) symmetry break supersymmetry dynamically.dual to the SU(N c ) theory.1.2 The SU(2) × SU(2) Theories.In the first part of this paper, (sections 2 -4), we extend Seiberg's results to the SU(2) 1 × SU(2) 2 theory. The theory we study has 2n SU(2) 1 fundamentals, 2m SU(2) 2 fundamentals, and one field transforming as a fundamental under both groups. We will refer to this theory as the [n, m] model. We will analyze the theory as n, m are varied 1 . As in the case of SUSY QCD, we will find that for small values of n and m, (n, m ≤ 2), the theory is confining. For larger values of n and m the theory can be in the non-Abelian Coulomb phase, and we construct dual descriptions for it. The analysis in this case is qualitatively different depending on whether n, m > 2, or only one of them is greater than 2. We discuss these different possibilities below. The Duality Regime.We begin our study of duality in section 2 by considering the [n, m] models with both n, m ≥ 3. In this case, each SU(2), considered separately, has N f > N c + 1 = 3 flavors, and one expects a dual theory to exist. In fact, with some thought, several theories can be constructed which could, potentially, have the same low-energy behavior as the original [n, m] theory (we will sometimes refer to this theory as the electric theory). For example, one can turn off, at first, the gauge coupling of the second gauge group. The resulting SU(2) gauge theory has a well known dual which has a global symmetry corresponding to the second SU(2). It is natural to guess that on gauging this symmetry one gets a theory which agrees with the electric one in the infra-red. One can now carry this process one step further and dualize the second SU(2) symmetry as well, thereby getting another dual theory. Note that by construction these theories have the same global symmetries as the original electric one, and the 't Hooft anomaly matching conditions for these symmetries are satisfied.Dualizing SU(2) 1 first, we construct two dual theories. One with gauge group SP (2n − 4) × SU(2) 2 , and the other with gauge group SP (2n − 4) × SP (4n + 2m...

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The renormalization of operators responsible for soft supersymmetry breaking is usually calculated by starting at some high scale and including only visible sector interactions in the evolution equations, while ignoring hidden sector interactions. Here we explain why this is correct only for the most trivial structures in the hidden sector, and discuss possible implications. This investigation was prompted by the idea of conformal sequestering. In that framework hidden sector renormalizations by nearly conformal dynamics are critical. In the original models of conformal sequestering it was necessary to impose hidden sector flavor symmetries to achieve the sequestered form. We present models which can evade this requirement and lead to no-scale or anomaly mediated boundary conditions; but the necessary structures do not seem generic. More generally, the ratios of scalar masses to gaugino masses, the µ-term, the Bµ-term, A-terms, and the gravitino mass can be significantly affected.

The effects of heavy mass thresholds on anomaly-mediated soft supersymmetry breaking terms are discussed. While heavy thresholds completely decouple to lowest order in the supersymmetry breaking, it is argued that they do affect the breaking terms at higher orders. The relevant contributions typically occur at lower order in the loop expansion compared to purely anomaly mediated contributions. The non decoupling contributions may be used to render models in which the only source of supersymmetry breaking is anomaly mediation viable, by generating positive contributions to the sleptons' masses squared. They can also be used to generate acceptable µ-and B-terms.