Electric Magnetic Duality in String Theory

TL;DR

This paper demonstrates that electric-magnetic duality in four-dimensional heterotic string theory is an exact symmetry of the equations of motion, enabling the construction of dual black hole solutions and suggesting a fundamental symmetry exchanging elementary strings and solitons.

Contribution

It establishes the exactness of electric-magnetic duality in the low energy effective field theory of heterotic string theory and constructs dual black hole solutions with both electric and magnetic charges.

Findings

Dual black hole solutions with electric and magnetic charges constructed.

Spectrum of extremal magnetically charged black holes similar to elementary string excitations.

Duality may be an exact symmetry exchanging strings and solitons in full string theory.

Abstract

The electric-magnetic duality transformation in four dimensional heterotic string theory discussed by Shapere, Trivedi and Wilczek is shown to be an exact symmetry of the equations of motion of low energy effective field theory even after including the scalar and the vector fields, arising due to compactification, in the effective field theory. Using this duality transformation we construct rotating black hole solutions in the effective field theory carrying both, electric and magnetic charges. The spectrum of extremal magnetically charged black holes turns out to be similar to that of electrically charged elementary string excitations. We also discuss the possibility that the duality symmetry is an exact symmetry of the full string theory under which electrically charged elementary string excitations get exchanged with magnetically charged soliton like solutions. This proposal might be made concrete following the suggestion of Dabholkar et. al. that fundamental strings may be regarded as soliton like classical solutions in the effective field theory.