Supersymmetric Dyons, Superstrings, and Rotating Wormholes

TL;DR

This paper constructs supersymmetric dyon solutions in string theory, explores their geometric properties, and reveals how spin influences curvature and frame dragging, illustrating gauge/gravity duality.

Contribution

It introduces new supersymmetric dyon solutions based on monopoles, connects them to string theory configurations, and analyzes their geometries with respect to spin effects.

Findings

Finite scalar curvature for non-spinning dyons

Frame dragging observed in spinning solutions

Curvature diverges along the spin axis as 1/ρ^2

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.