Anomalies and effective lagrangians of superconducting cosmic strings

We study the effective langrangians of superconducting cosmic strings and the underlying anomaly structure leading to various effects. We show that fermionic superconducting cosmic (Nielsen-Olesen) strings arise as a consequence of mixed anomaly of the form E.B' where E is the electromagnetic field strength and B' the core flux of the string. We show how this controls superconductivity, the index theorems, topological mass terms on domain walls, and string-axion interactions. We contrast this to global strings with Chern-Simons currents. (orig.)