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 $SO\left(32\right)$ 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 nonvanishing spin. In the case of the vanishing spin, the scalar curvature is finite everywhere. In the case of the nonvanishing 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.