[en] A conjecture relating instanton calculus in four dimensional supersymmetric theories and the deformation theory of Lagrangian submanifolds in C^2r invariant under a (subgroup of) Sp(2r,Z) is formulated. This is a four dimensional counterpart of the mirror symmetry of topological strings (relating Gromov-Witten invariants and generalized variations of Hodge structure). (orig.)

[en] The physics potential is briefly summarized for an e⁺e^- linear collider operating at center-of-mass energies up to √(s) = 1 TeV and delivering integrated luminosities up to ∫ L = 0.5 ab^-1 in one to two years. This machine will allow us to perform precision studies of the top quark and the electroweak gauge bosons at the per-mille level. It will be an ideal instrument to investigate the properties of the Higgs boson and to establish essential elements of the Higgs mechanism as the fundamental mechanism for breaking the electroweak symmetries. In the area beyond the standard model, new particles and their interactions can be discovered and explored comprehensively. In supersymmetric theories, the mechanism of the symmetry breaking can be investigated experimentally and the underlying unified theory can be reconstructed. The high precision allows stable extrapolations up to scales near the Planck mass. (orig.)

[en] We develop some useful techniques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkaehler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkaehler periods. We also reduce these volumes for a large class of hyperkaehler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on R⁴ and ALE manifolds, Hitchin spaces, and moduli spaces of (parabolic) Higgs bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of the volume reduces to a summation over solutions of Bethe ansatz equations for the non-linear Schroedinger system. We discuss some applications of our results. (orig.)

[en] To establish the Higgs mechanism sui generis experimentally, the Higgs self-interaction potential must be reconstructed. This task requires the measurement of the trilinear and quadrilinear self-couplings, as predicted in the standard model or in supersymmetric theories. The couplings can be probed in multiple Higgs production at high-luminosity e⁺e^- linear colliders. We present the theoretical analysis for the production of neutral Higgs-boson pairs in the relevant channels of double Higgs-strahlung and associated multiple Higgs production. (orig.)