Magnetic interactions of D-branes and Wess-Zumino terms in Super Yang-Mills effective actions

There is a close relation between classical supergravity and quantum SYM descriptions of interactions between separated branes. In the case of D3 branes the equivalence of leading-order potentials is due to non-renormalization of the F4 term in N=4 SYM theory. Here we point out the existence of another special non-renormalized term in quantum SYM effective action. This term reproduces the interaction potential between electric charge of a D3-brane probe and magnetic charge of a D3-brane source, represented by the Chern-Simons part of the D-brane action. This unique Wess-Zumino term depends on all six scalar fields and originates from a phase of the euclidean fermion determinant in SYM theory. It is manifestly scale invariant (i.e. is the same for large and small separations between branes) and can not receive higher loop corrections in gauge theory. Maximally supersymmetric SYM theories in D=p+1>4 contain mixed WZ terms which depend on both scalar and gauge field backgrounds, and which reproduce the corresponding CS terms in the supergravity interaction potentials between separated Dp-branes for p>3. Purely scalar WZ terms appear in other cases, e.g., in half less supersymmetric gauge theories in various dimensions describing magnetic interactions between Dp and D(6−p) branes.