Exactly solvable string models of curved space-time backgrounds

TL;DR

This paper introduces a new class of exactly solvable 4D string models with curved backgrounds, including rotating flux-tube universes, and analyzes their spectra, dualities, and physical properties, advancing understanding of string solutions in curved spacetime.

Contribution

It presents a novel 3-parameter family of exact 4D string backgrounds, solves the corresponding models, and explores their physical implications and dualities, providing one of the first explicit D=4 curved space-time string solutions.

Findings

Includes dilatonic and Kaluza-Klein Melvin solutions

Analyzes tachyonic instabilities and gyromagnetic ratios

Discusses singularities and duality relations

Abstract

We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the dilatonic (a=1) and Kaluza-Klein (a=\sqrt 3) Melvin solutions and the uniform magnetic field solution, as well as some singular space-times. Solvability of the string sigma model is related to its connection via duality to a simpler model which is a ``twisted" product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model (tachyonic instabilities in the spectrum, gyromagnetic ratios, issue of singularities, etc.). It provides one of the first examples of a consistent solvable conformal string model with explicit D=4 curved space-time interpretation.