Dyons, Superstrings, and Wormholes: Exact Solutions of the Non-Abelian Dirac-Born-Infeld Action

Abstract

We construct dyon solutions on coincidentD4-branes, obtained by applyingT-duality transformations to type ISO(32)superstring theory in 10 dimensions. These solutions, which are exact, are obtained from an action comprising the non-Abelian Dirac-Born-Infeld action and a Wess-Zumino-like action. When one spatial dimension of theD4-branes is taken to be vanishingly small, the dyons are analogous to the ’t Hooft/Polyakov monopole residing in a3+1-dimensional spacetime, where the component of the Yang-Mills potential transforming as a Lorentz scalar is reinterpreted as a Higgs boson transforming in the adjoint representation of the gauge group. Applying aT-duality transformation to the vanishingly small spatial dimension, we obtain a collection ofD3-branes, not all of which are coincident. Two of theD3-branes, distinct from the others, acquire intrinsic, finite curvature and are connected by a wormhole. The dyons possess electric and magnetic charges whose values on eachD3-brane are the negative of one another. The gravitational effects, which arise after theT-duality transformation, occur despite the fact that the action of the system does not explicitly include the gravitational interaction. These solutions provide a simple example of the subtle relationship between the Yang-Mills and gravitational interactions, that is, gauge/gravity duality.