Charged string solutions with dilaton and modulus fields

TL;DR

This paper derives charged, spherically symmetric solutions in heterotic string theory with dilaton and modulus fields, analyzing their stability, energy, and behavior across different coupling regimes considering perturbative and non-perturbative effects.

Contribution

It presents new stable, finite energy solutions incorporating scale-dependent dilaton and modulus fields with threshold corrections and non-perturbative potentials in heterotic string theory.

Findings

Stable electric solutions exist in weak coupling regions.

Magnetic solutions are limited to specific threshold correction parameters.

Non-perturbative potential fixes asymptotic field values.

Abstract

We find charged, abelian, spherically symmetric solutions (in flat space-time) corresponding to the effective action of $D=4$ heterotic string theory with scale-dependent dilaton $\p$ and modulus $\vp$ fields. We take into account perturbative (genus-one), moduli-dependent `threshold' corrections to the coupling function $f(\p,\vp)$ in the gauge field kinetic term $f(\p,\vp) F^2_{\m\n}$, as well as non-perturbative scalar potential $V(\p, \vp)$, e.g. induced by gaugino condensation in the hidden gauge sector. Stable, finite energy, electric solutions (corresponding to on abelian subgroup of a non-abelian gauge group) have the small scale region as the weak coupling region ($\phi\ra -\infty$) with the modulus $\vp$ slowly varying towards smaller values. Stable, finite energy, abelian magnetic solutions exist only for a specific range of threshold correction parameters. At small scales they correspond to the strong coupling region ($\p\ra \infty$) and the compactification region ($\vp\ra 0$). The non-perturbative potential $V$ plays a crucial role at large scales, where it fixes the asymptotic values of $\phi$ and $\vp$ to be at the minimum of $V$.