Supersymmetric Dyons, Superstrings, and Rotating Wormholes

Abstract

We construct supersymmetric dyon solutions based on the 't Hooft/Polyakov monopole. We show that these solutions satisfy $\kappa$ symmetry constraints and can, therefore be generalized to supersymmetric solutions of type I SO(32) string theory. After applying a T-duality transformation to these solutions, we obtain two $D3$-branes connected by a wormhole, embedded in an M5 brane. We analyze the geometries of each $D3$-brane for two cases, one corresponding to a dyon with vanishing spin, and the other corresponding to a magnetic monopole with non-vanishing spin. In the case of vanishing spin, the scalar curvature is finite, everywhere, In the case of non-vanishing spin, we find a frame dragging effect due to the spin. We also find that the scalar curvature diverges along the spin quantization axis, as $1/\rho^2$, $\rho$ being the cylindrical, radial coordinate defined with respect to the spin axis. These solutions demonstrate the subtle relationship between the Yang-Mills and gravitational interactions, i.e., gauge/gravity duality.