Brane Gases on K3 and Calabi-Yau Manifolds

TL;DR

The paper extends Brane Gas Cosmology (BGC) beyond toroidal compactifications to manifolds with non-trivial holonomy, focusing on K3 and Calabi-Yau backgrounds to improve connections with particle physics. By leveraging dualities among M-theory branches, it constructs brane gas scenarios that yield ${\mathcal N}=2$ four-dimensional theories on K3×T^2 and, more broadly, on Calabi-Yau threefolds, while preserving BGC’s mechanism for dynamical dimensional reduction via winding modes. It shows that winding on higher-dimensional cycles (e.g., 2-cycles on K3) can drive decompactification even without one-cycles, and articulates a network of dualities that links Type IIA on K3 and heterotic $E_8\times E_8$ on T^4 to CY compactifications, offering an existence proof of CY-compatible BGC. The results provide a concrete step toward integrating string cosmology with realistic particle physics and motivate exploring ${\mathcal N}=1$ realizations in future work, using CY geometry and dualities to bridge early-universe dynamics with low-energy phenomenology.

Abstract

We initiate the study of Brane Gas Cosmology (BGC) on manifolds with non-trivial holonomy. Such compactifications are required within the context of superstring theory in order to make connections with realistic particle physics. We study the dynamics of brane gases constructed from various string theories on background spaces having a K3 submanifold. The K3 compactifications provide a stepping stone for generalising the model to the case of a full Calabi-Yau three-fold. Duality symmetries are discussed within a cosmological context. Using a duality, we arrive at an N=2 theory in four-dimensions compactified on a Calabi-Yau manifold with SU(3) holonomy. We argue that the Brane Gas model compactified on such spaces maintains the successes of the trivial toroidal compactification while greatly enhancing its connection to particle physics. The initial state of the universe is taken to be a small, hot and dense gas of p-branes near thermal equilibrium. The universe has no initial singularity and the dynamics of string winding modes allow three spatial dimensions to grow large, providing a possible solution to the dimensionality problem of string theory.