Dualities in Five Dimensions and Charged String Solutions

TL;DR

This paper explores dualities in five-dimensional supergravity derived from string theories, presenting charged string solutions and demonstrating how topology changes relate to string-particle duality.

Contribution

It introduces magnetically charged string solutions in five dimensions and connects dualities with topological changes using Poincare duality.

Findings

Magnetically charged solutions with charges on S^3 and S^2 spheres.

Demonstration of topology change from S^3 to S^2 in dualities.

Support for string-string duality in six dimensions.

Abstract

We consider an eleven dimensional supergravity compactified on $K3\times T^2$ and show that the resulting five dimensional theory has identical massless states as that of heterotic string compactified on a specific five torus $T^5$. The strong-weak coupling duality of the five dimensional theory is argued to represent a ten dimensional Type $IIA$ string compactified on $K3 \times S^1$, supporting the conjecture of string-string duality in six dimensions. In this perspective, we present magnetically charged solution of the low energy heterotic string effective action in five dimensions with a charge defined on a three sphere $S^3$ due to the two form potential. We use the Poincare duality to replace the antisymmetric two form with a gauge field in the effective action and obtain a string solution with charge on a two sphere $S^2$ instead of that on a three sphere $S^3$ in the five dimensional spacetime. We note that the string-particle duality is accompanied by a change of topology from $S^3$ to $S^2$ and viceversa.