Non-standard embedding and five-branes in heterotic M-Theory

TL;DR

This work extends heterotic M-theory vacua to include non-standard embeddings and bulk five-branes, providing a consistent 11D background via a double expansion in $\epsilon_S$ and $\epsilon_R$ and a Calabi–Yau harmonic-mode analysis. It shows that non-standard embeddings enlarge possible gauge breakings and introduce new brane-world gauge sectors, with five-branes generating non-perturbative gauge-threshold corrections and moduli tied to brane positions. The resulting 5D gauged supergravity and 4D effective actions acquire novel features: piecewise-linear background profiles, brane-induced gauging, and a spectrum that includes both brane-localized and bulk degrees of freedom, organized into multi-domain-wall vacua. These findings broaden the landscape of $N=1$ vacua in strongly coupled heterotic M-theory and highlight the phenomenological implications of brane-world sectors and position-dependent couplings.

Abstract

We construct vacua of M-theory on S^1/Z_2 associated with Calabi-Yau three-folds. These vacua are appropriate for compactification to N=1 supersymmetry theories in both four and five dimensions. We allow for general E_8 x E_8 gauge bundles and for the presence of five-branes. The five-branes span the four-dimensional uncompactified space and are wrapped on holomorphic curves in the Calabi-Yau space. Properties of these vacua, as well as of the resulting low-energy theories, are discussed. We find that the low-energy gauge group is enlarged by gauge fields that originate on the five-brane world-volumes. In addition, the five-branes increase the types of new E_8 x E_8 breaking patterns allowed by the non-standard embedding. Characteristic features of the low-energy theory, such as the threshold corrections to the gauge kinetic functions, are significantly modified due to the presence of the five-branes, as compared to the case of standard or non-standard embeddings without five-branes.

Figures (3)

• Figure 1: Orbifold interval with boundaries at $0$, $\pi\rho$ and $N$ five-branes at $x_1,\dots ,x_N$. The mirror interval from $0$ to $-\pi\rho$ is suppressed in this diagram.
• Figure 2: Intersection of a five-brane wrapped on the holomorphic cycle ${\cal C}_2^{(n)}$ and a four-cycle ${\cal C}_4$. In this example the five-brane contributes two units of magnetic charge on ${\cal C}_4$.
• Figure 3: Orbifold dependence of a massless mode $(\sqrt{2}/\pi\epsilon_S)b$ for four five-branes at $(z_1,z_2,z_3,z_4)=(0.2,0.6,0.8,0.8)$ with charges $(\beta^{(1)},\beta^{(2)},\beta^{(3)},\beta^{(4)})=(1,1,1,1)$ and instanton numbers $(\beta^{(0)},\beta^{(4)})=(-1,-3)$.