Covariant Harmonic Supergraphity for N = 2 Super Yang--Mills Theories

We review the background field method for general N = 2 super Yang-Mills theories formulated in the N = 2 harmonic superspace. The covariant harmonic supergraph technique is then applied to rigorously prove the N=2 non-renormalization theorem as well as to compute the holomorphic low-energy action for the N = 2 SU(2) pure super Yang-Mills theory and the leading non-holomorphic low-energy correction for N = 4 SU(2) super Yang-Mills theory.Comment: 17 pages, LAMUPHYS LaTeX, no figures; based on talks given by I. Buchbinder and S. Kuzenko at the International Seminar ``Supersymmetries and Quantum Symmetries'', July 1997, Dubna; to be published in the proceeding

Harmonicity in N=4 supersymmetry and its quantum anomaly

The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N=4 Weyl superfield, computed by N=4 topological amplitudes. These equations can also be derived on the string side, exhibiting an anomaly from world-sheet boundary contributions that leads to recursion relations for the non-analytic part of the couplings.Comment: 36 page

Worldline Superfield Actions for N=2 Superparticles

We propose doubly supersymmetric actions in terms of n=2(D-2) worldline superfields for N=2 superparticles in D=3,4 and Type IIA D=6 superspaces. These actions are obtained by dimensional reduction of superfield actions for N=1 superparticles in D=4,6 and 10, respectively. We show that in all these models geometrodynamical constraints on target superspace coordinates do not put the theory on the mass shell, so the actions constructed consistently describe the dynamics of the corresponding N=2 superparticles. We also find that in contrast to the IIA D=6 superparticle a chiral IIB D=6 superparticle, which is not obtainable by dimensional reduction from N=1, D=10, is described by superfield constraints which produce dynamical equations. This implies that for the IIB D=6 superparticle the doubly supersymmetric action does not exist in the conventional form.Comment: Latex, 20 pp. Minor corrections, acknowledgements adde

On pseudo-hyperk\"ahler prepotentials

An explicit surjection from a set of (locally defined) unconstrained holomorphic functions on a certain submanifold of (Sp_1(C) \times C^{4n}) onto the set HK_{p,q} of local isometry classes of real analytic pseudo-hyperk\"ahler metrics of signature (4p,4q) in dimension 4n is constructed. The holomorphic functions, called prepotentials, are analogues of K\"ahler potentials for K\"ahler metrics and provide a complete parameterisation of HK_{p,q}. In particular, there exists a bijection between HK_{p,q} and the set of equivalence classes of prepotentials. This affords the explicit construction of pseudo-hyperk\"ahler metrics from specified prepotentials. The construction generalises one due to Galperin, Ivanov, Ogievetsky and Sokatchev. Their work is given a coordinate-free formulation and complete, self-contained proofs are provided. An appendix provides a vital tool for this construction: a reformulation of real analytic G-structures in terms of holomorphic frame fields on complex manifolds.Comment: 53 pages; v2: minor amendments to Def.4.1 and Theorem 4.5; a paragraph inserted in the proof of the latter; V3: minor changes; V4: minor changes/ typos corrected for journal versio

Point contact spectroscopy of hopping transport: effects of a magnetic field

The conductance of a point contact between two hopping insulators is expected to be dominated by the individual localized states in its vicinity. Here we study the additional effects due to an external magnetic field. Combined with the measured conductance, the measured magnetoresistance provides detailed information on these states (e.g. their localization length, the energy difference and the hopping distance between them). We also calculate the statistics of this magnetoresistance, which can be collected by changing the gate voltage in a single device. Since the conductance is dominated by the quantum interference of particular mesoscopic structures near the point contact, it is predicted to exhibit Aharonov-Bohm oscillations, which yield information on the geometry of these structures. These oscillations also depend on local spin accumulation and correlations, which can be modified by the external field. Finally, we also estimate the mesoscopic Hall voltage due to these structures.Comment: 7 pages, 5 figur

Oscillatory regimes of the thermomagnetic instability in superconducting films

The stability of superconducting films with respect to oscillatory precursor modes for thermomag- netic avalanches is investigated theoretically. The results for the onset threshold show that previous treatments of non-oscillatory modes have predicted much higher thresholds. Thus, in film supercon- ductors, oscillatory modes are far more likely to cause thermomagnetic breakdown. This explains the experimental fact that flux avalanches in film superconductors can occur even at very small ramping rates of the applied magnetic field. Closed expressions for the threshold magnetic field and temperature, as well oscillation frequency, are derived for different regimes of the oscillatory thermomagnetic instability.Comment: 5 pages, 5 figure