Dipole Moments of Black Holes and String States

TL;DR

This paper tests the conjectured equivalence between string states and extremal black holes by comparing their dipole moments, finding perfect agreement across BPS, intermediate, and non-BPS states, thus supporting the duality.

Contribution

It provides the first detailed comparison of dipole moments for black holes and string states across different multiplet types, including non-BPS states, strengthening the black-hole/string-state duality.

Findings

Black hole gyromagnetic ratios match string states for BPS and intermediate multiplets.

Electric and magnetic dipole moments of black holes are consistent with string dualities.

Non-supersymmetric extremal black holes also agree with non-BPS string states.

Abstract

As a further test of the conjectured equivalence of string states and extremal black holes, we compute the dipole moments of black holes with arbitrary spin and superspin in D=4,N=4 supergravity coupled to 22 vector multiplets and compare them with the dipole moments of states in the heterotic string on $T^6$ or the Type IIA string on $K3 \times T^2$. Starting from a purely bosonic black hole with Kerr angular momentum L, the superpartners are generated by acting with fermion zero modes, thus filling out the complete supermultiplet. $L$ is then identified with the superspin. On the heterotic side, elementary states belong only to short to long multiplets, but Type IIA elementary states can belong to intermediate multiplets as well. We find that the black hole gyromagnetic ratios are in perfect agreement with the string states not only for the BPS states belonging to short multiplets but also for those belonging to intermediate multiplets. In fact, these intermediate multiplets provide a stronger test of the black-hole/string-state equivalence because the gyromagnetic ratios are not determined by supersymmetry alone, in contrast to those of the short multiplets. We even find agreement between the non-supersymmetric (but still extremal) black holes and non-BPS string states belonging to long supermultiplets. In addition to magnetic dipole moments we also find electric dipole moments even for purely electrically charged black holes. The electric dipole moments of the corresponding string states have not yet been calculated directly but are consistent with heterotic/Type IIA duality.