Visible Branes with Negative Tension in Heterotic M-Theory

TL;DR

The paper addresses whether heterotic M-theory can host brane configurations compatible with Ekpyrotic cosmology, namely a negative-tension visible brane, a positive-tension hidden brane, and positive-tension bulk five-branes. It develops the 5D effective theory for setups with and without bulk five-branes, expresses brane tensions in terms of second Chern classes of the tangent bundle and vector bundles, and imposes the topological condition $c_{2}(TX) - c_{2}(V^{1}) - c_{2}(V^{2}) + W = 0$ with $W$ the bulk five-brane class. By constructing explicit non-standard embeddings on elliptically fibered Calabi–Yau three-folds (e.g., bases $B=dP_{8}$ and $B=F_{r}$) and analyzing curve volumes, the authors produce vacua with $\\alpha^{(1)}<0$, $\\alpha^{(2)}>0$, and $\\beta>0$, and show that the ratio $\\beta/|\\alpha^{(1)}|$ can be made arbitrarily small in large classes of models. These results demonstrate the feasibility of Ekpyrotic-like cosmologies within heterotic M-theory and counter claims that such tension configurations are impossible; the constructions extend to other elliptic fibrations and gauge choices, underscoring the framework’s robustness.

Abstract

It is shown that there exist large classes of BPS vacua in heterotic M-theory which have negative tension on the visible orbifold plane, positive tension on the hidden plane and positive tension, physical five-branes in the bulk space. Explicit examples of such vacua are presented. Furthermore, it is demonstrated that the ratio, beta/|alpha|, of the bulk five-brane tension to the visible plane tension can, for several large classes of such vacua, be made arbitrarily small. Hence, it is straightforward to find vacua with the properties required in the examples of the Ekpyrotic theory of cosmology - a visible brane with negative tension and beta/|alpha| small. This contradicts recent claims in the literature.