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 de scriptions of interactions between separated branes. In the case of D3 bran es the equivalence of leading-order potentials is due to non-renormalizatio n of the F-4 term in N = 4 SYM theory. Here we point out the existence of a nother special non-renormalized term in quantum SYM effective action. This term reproduces the interaction potential between electric charge of a D3-b rane probe and magnetic charge of a D3-brane source, represented by the Che m-Simons part of the D-brane action. This unique Wess-Zumino term depends o n all six scalar fields and originates from a phase of the euclidean fermio n 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 hi gher loop corrections in gauge theory. Maximally supersymmetric SYM theorie s in D = p + 1 > 4 contain mixed WZ terms which depend on both scalar and g auge field backgrounds, and which reproduce the corresponding CS terms in t he supergravity interaction potentials between separated Dp-branes for p > 3. Purely scalar WZ terms appear in other cases, e.g., in half less supersy mmetric gauge theories in various dimensions describing magnetic interactio ns between Dp and D(6 - p) branes. (C) 2000 Published by Elsevier Science B .V. All rights reserved.