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Moving Five-Branes in Low-Energy Heterotic M-Theory

Edmund J. Copeland, James Gray, Andre Lukas

TL;DR

The paper addresses how moving five-branes in low-energy heterotic M-theory shape four-dimensional cosmologies by introducing a moving brane modulus into the 4D effective action. The authors develop a cosmological moduli-space Lagrangian that yields a family of solutions where brane motion drives a transition between two rolling radii regimes and generally pushes the system toward strong coupling. They present an explicit negative-time branch example in which a brane collision triggers a small-instanton transition, illustrating a brane-induced non-singular transition and linking to pre-big-bang and ekpyrotic-inspired scenarios. The framework generalizes to include curvature, fluids, or multiple branes, offering a versatile platform for brane-world cosmology in heterotic M-theory.

Abstract

We construct cosmological solutions of four-dimensional effective heterotic M-theory with a moving five-brane and evolving dilaton and T modulus. It is shown that the five-brane generates a transition between two asymptotic rolling-radii solutions. Moreover, the five-brane motion always drives the solutions towards strong coupling asymptotically. We present an explicit example of a negative-time branch solution which ends in a brane collision accompanied by a small-instanton transition. The five-dimensional origin of some of our solutions is also discussed.

Moving Five-Branes in Low-Energy Heterotic M-Theory

TL;DR

The paper addresses how moving five-branes in low-energy heterotic M-theory shape four-dimensional cosmologies by introducing a moving brane modulus into the 4D effective action. The authors develop a cosmological moduli-space Lagrangian that yields a family of solutions where brane motion drives a transition between two rolling radii regimes and generally pushes the system toward strong coupling. They present an explicit negative-time branch example in which a brane collision triggers a small-instanton transition, illustrating a brane-induced non-singular transition and linking to pre-big-bang and ekpyrotic-inspired scenarios. The framework generalizes to include curvature, fluids, or multiple branes, offering a versatile platform for brane-world cosmology in heterotic M-theory.

Abstract

We construct cosmological solutions of four-dimensional effective heterotic M-theory with a moving five-brane and evolving dilaton and T modulus. It is shown that the five-brane generates a transition between two asymptotic rolling-radii solutions. Moreover, the five-brane motion always drives the solutions towards strong coupling asymptotically. We present an explicit example of a negative-time branch solution which ends in a brane collision accompanied by a small-instanton transition. The five-dimensional origin of some of our solutions is also discussed.

Paper Structure

This paper contains 7 sections, 35 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Four-dimensional effective action
  3. Cosmological solutions with a moving five-brane
  4. Equations of motion and their solutions
  5. Properties and asymptotic behaviour of the solutions
  6. An explicit example
  7. Generalisations and Outlook

Figures (3)

  • Figure 1: It is shown how the ellipse of possible expansion powers $(p_\beta ,p_\phi )$ is mapped into itself under the influence of the moving five-brane. Points related by the map may be joined with a straight line of slope $-3$ as indicated by the arrows. There are two fixed points under this map on the ellipse given by $\delta =p_{\beta} - p_{\alpha}=0$. These points correspond to solutions which are related to separating solutions in five dimensions. In these special cases the five-brane modulus $z$ is constant.
  • Figure 2: Time-behaviour of $\beta$ (upper curve) and $\phi$ (lower curve) for the example specified in the text.
  • Figure 3: Time-behaviour of the five-brane position modulus $z$ for the example specified in the text. The boundaries are located at $z=0,1$ and the five-brane collides with the $z=0$ boundary at $|t/T|\simeq 1$.