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Register a new userDyons, Superstrings, and Wormholes
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Authors
Edward A. Olszewski
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We construct dyon solutions on a collection of coincident D4-branes, obtained by applying the group of T-duality transformations to a type I SO(32) superstring theory in 10 dimensions. The dyon solutions, which are exact, are obtained from an action consisting of the non-abelian Dirac-Born-Infeld action and Wess-Zumino-like action. When one of the spatial dimensions of the D4-branes is taken to be vanishingly small, the dyons are analogous to the t Hooft/Polyakov monopole residing in a 3+1 dimensional spacetime, where the component of the Yang-Mills potential transforming as a Lorentz scalar is re-interpreted as a Higgs boson transforming in the adjoint representation of the gauge group. We next apply a T-duality transformation to the vanishingly small spatial dimension. The result is a collection of D3-branes not all of which are coincident. Two of the D3-branes which are separated from the others acquire intrinsic, finite, curvature and are connected by a wormhole. The dyon possesses electric and magnetic charges whose values on each D3-brane are the negative of one another. The gravitational effects, which arise after the T-duality transformation, occur despite the fact that the Lagrangian density from which the dyon solutions have been obtained does not explicitly include the gravitational interaction. These solutions provide a simple example of the subtle relationship between the Yang-Mills and gravitational interactions, i.e. gauge/gravity duality.
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We construct dyon solutions in SU(N) with topological electric and magnetic charge. Assuming a |Phi|^4-like potential for the Higgs field we show that the mass of the dyons is relatively insensitive to the coupling parameter lambda characterizing the potential. We then apply the methodology of constructing dyon solutions in SU(N) to G2. In order to define the electromagnetic field consistently in the manner that we propose we find that dyon solutions exist only when G2 is considered under the action of its maximal and regular subgroup SU(3). In this case we find two different types of dyons, one of which has properties identical to dyons in SU(3). The other dyon has some properties which are seemingly atypical, e.g. the magnetic charge g_m = 4 pi 3/e, which differs from the t Hooft/Polyakov monopole where g_m = 4 pi 1/e.
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