We discuss the use of the spectral asymmetry of the Dirac Hamiltonian as a means to determine the rate of anomalous creation of chiral fermions in the presence of background gauge and scalar fields. The (suitably modified) spectral asymmetry is computed explicitly for a wide class of Hamiltonians in terms of functionals of the restriction of the Hamiltonian to lower-dimensional spaces. The result is used to determine the anomalous charge which gives rise to superconductivity of cos- mic or axion strings (vortices). It is shown that superconductivity of cosmic strings is present even when the usual finite-energy requirement is dropped and open-space boundary conditions are adopted instead. This is shown to apply to the case of axion strings as well.

• Received 16 February 1988

DOI:https://doi.org/10.1103/PhysRevD.38.1108