Sphaleron of a 4 dimensional SO(4) Higgs model

We construct the finite energy path between topologically distinct vacua of a 4 dimensional SO(4) Higgs model which is known to support an instanton, and show that there is a sphaleron with Chern-Simons number N_CS=1/2 at the top of the energy barrier. This is carried out using the original geometric loop construction of Manton.Comment: 9 pages, 2 figures, LaTex format, minor text corrections. To be published in Phys. Lett.

Quantum Tunneling and Phase Transitions in Spin Systems with an Applied Magnetic Field

Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions can be interpreted as first- or second-order phase transitions depending on the anisotropy and magnetic parameters defining the system in an effective Lagrangian description.Comment: 18 pages, 7 figure

Significance of zero modes in path--integral quantization of solitonic theories with BRST invariance

The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1+2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to - the one-loop approximation.Comment: 16 pages, LaTe

N=2 String-String Duality and Holomorphic couplings

We review aspects of N=2 duality between the heterotic and the type IIA string. After a description of string duality intended for the non-specialist the computation of the heterotic prepotential and the $F_1$ function for the ST, STU and STUV model (V a Wilson line) and the matching with the Calabi-Yau instanton expansions are given in detail. Relations with BPS spectral sums in various connections are pointed out.Comment: 86 pages, late

Quantum Tunneling of Spin Particles in Periodic Potentials with Asymmetric Twin Barriers

The tunneling effect of a periodic potential with an asymmetric twin barrier per period is calculated using the instanton method. The model is derived from the Hamiltonian of a small ferromagnetic particle in an external magnetic field using the spin-coherent-state path integral. The instantons in two neighbouring barriers differ and lead to different level shifts $\triangle\epsilon_1, \triangle\epsilon_2$. We derive with Bloch theory the energy spectrum which has formally the structure of an energy band. The spectrum depends on both level shifts. The removal of Kramer's degeneracy by an external magnetic field is discussed. In addition we find a new kind of quenching of macroscopic quantum coherence which is irrelevant to Kramer's degeneracy.Comment: 18 pages, LaTex, one figur