Abstract Let $$A/{\mathbb {Q}}$$ A / Q be an abelian variety such that $$A({\mathbb {Q}}) =\{0_A\}$$ ( ) = { 0 } . $$\ell $$ <mm...

We derive anomaly constraints for Abelian and non-Abelian discrete symmetries using the path integral approach. We survey anomalies of discrete symmetries in heterotic orbifolds and find a new relation between such anomalies and the socalled ‘anomalous’ U(1).

The topology assumed by most authors for a spacelike hypersurface in a spacetime containing a monopole is generally R3−{0}; save for the surface S2 isolating the monopole, this space is unbounded. For such a topology, a consistency relation of de Rham’s theorems shows that a single isolated monopole cannot exist. Monopoles, with charge ±m, if they exist at all, must occur in pairs having opposi...

We derive a version of non-Abelian Stokes theorem for SU(2) gauge fields in which neither additional integration nor surface ordering are required. The path ordering is eliminated by introducing the instantaneous color orientation of the flux. We also derive the non-Abelian Stokes theorem on the lattice and discuss various terms contributing to the trace of the Wilson loop. Introduction The usu...

We prove a strong form of the Brumer–Stark Conjecture and, as a consequence, a strong form of Rubin’s integral refinement of the abelian Stark Conjecture, for a large class of abelian extensions of an arbitrary characteristic p global field k. This class includes all the abelian extensions K/k contained in the compositum kp∞ := kp · k∞ of the maximal pro-p abelian extension kp/k and the maximal...