Electric dipole moment induced by a QCD instanton in an external magnetic field

In the chiral magnetic effect, there is a competition between a strong magnetic field, which tends to project positively charged particles to have spin aligned along the magnetic field, and a chirality imbalance which may be produced locally by a topologically nontrivial gauge field such as an instanton. We study the properties of the Euclidean Dirac equation for a light fermion in the presence of both a constant Abelian magnetic field and an SU(2) instanton. In particular, we analyze the zero modes analytically in various limits, both on R4 and on the four-torus, in order to compare with recent lattice QCD results, and study the implications for the electric dipole moment.