Book Description

Historically, the theory of monopoles and dyons has been plagued with nonlocality and broken Lorentz covariance, leading to difficulty in calculations of amplitudes involving magnetic currents. We present the Zwanziger two-gauge formalism that addresses these problems, and use spinor helicity methods to extract results in dyon-dyon and light-light scattering. Furthermore, we examine interacting Abelian theories at low energies and show that holomorphically normalized photon helicity amplitudes transform into dual amplitudes under SL(2,Z) as modular forms with weights that depend on the external photon helicities and the number of internal photon lines. Even though the amplitudes are not duality invariant, their squares are; we explicitly verify the duality transformation at one loop by comparing the amplitudes of an electron and the dyon that is its SL(2,Z) image, and extend the invariance of squared amplitudes order by order in perturbation theory. We demonstrate that S-duality is a property of all low-energy effective Abelian theories with electric and/or magnetic charges and see how the duality generically breaks down at high energies. A brief discussion of dualities, the Zwanziger formalism, and the spinor helicity method is also presented in the contexts of the Witten effect, the modular group, electric dipole moments, gauge anomalies, and non-Abelian magnetic charge. We also explore a new class of natural models which ensure the one-loop divergences in the Higgs mass are cancelled. The top-partners that cancel the top loop are new gauge bosons, and the symmetry relation that ensures the cancellation arises at an infrared fixed point. Such a cancellation mechanism can, a la Little Higgs models, push the scale of new physics that completely solves the hierarchy problem up to 5-10 TeV. When embedded in a supersymmetric model, the stop and gaugino masses provide the cutoffs for the loops, and the mechanism ensures a cancellation between the stop and gaugino mass dependence of the Higgs mass parameter.