Dual Heterotic Black-Holes in Four and Two Dimensions

TL;DR

This paper explores how certain four-dimensional heterotic black-hole solutions can be transformed into two-dimensional solutions using duality transformations, revealing a connection between different dimensional models in string theory.

Contribution

It demonstrates a method to connect 4D and 2D heterotic black-hole solutions via duality transformations and changes in harmonic functions, extending to the FHSV model.

Findings

Connected 4D and 2D black-hole solutions through dualities.

Showed the role of harmonic function asymptotics in dimensional transition.

Applied the mechanism to the FHSV model.

Abstract

We consider a class of extremal and non-extremal four-dimensional black-hole solutions occuring in toroidally compactified heterotic string theory, whose ten-dimensional interpretation involves a Kaluza-Klein monopole and a five-brane. We show that these four-dimensional solutions can be connected to extremal and non-extremal two-dimensional heterotic black-hole solutions through a change in the asymptotic behaviour of the harmonic functions associated with the Kaluza-Klein monopole and with the five-brane. This change in the asymptotic behaviour can be achieved by a sequence of S and T-S-T duality transformations in four dimensions. These transformations are implemented by performing a reduction on a two-torus with Lorentzian signature. We argue that the same mechanism can be applied to extremal and non-extremal black-hole solutions in the FHSV model.