Supergravity Fluxbranes in Various Dimensions

TL;DR

This paper explores fluxbrane solutions in various dimensions within Einstein-antisymmetric form-dilaton theories, deriving a master equation, analyzing solution behaviors, and discussing specific supergravity cases.

Contribution

It derives a universal master equation for fluxbrane solutions, analyzes their properties, and provides new insights into their behavior across different dimensions and supergravity theories.

Findings

A non-linear ODE admits an analytic singular solution serving as an attractor.

Globally regular solutions exist and are demonstrated numerically.

Maximally smeared fluxbranes have closed-form solutions obtainable via U-duality.

Abstract

We investigate fluxbrane solutions to the Einstein-antisymmetric form-dilaton theory in arbitrary space-time dimensions for a transverse space of cylindrical topology $S^k\times R^n$, corresponding to smeared and unsmeared solutions. A master equation for a single metric function is derived. This is a non-linear second-order ordinary differential equation admitting an analytic solution, singular at the origin, which serves as an attractor for globally regular solutions, whose existence is demonstrated numerically. For all fluxbranes of different levels of smearing the metric function diverges at infinity as the same power of the radial coordinate except for the maximally smeared case, where a global solution is known in closed form and can be obtained algebraically using U-duality. The particular cases of F6 and F3 fluxbranes in D=11 supergravity and fluxbranes in IIA, IIB supergravities are discussed.