Beyond the Standard Embedding in M-Theory on S^1/Z_2

TL;DR

The paper addresses extending Horava–Witten M-theory to nonstandard embeddings in the $E_8\times E_8$ vacuum by deriving a 4D $N=1$ effective theory from compactifications on $X\times S^1/Z_2$ and solving the Bianchi identity for the 3-form background. It shows that gauge couplings can take the form $\frac{1}{g_{(k)}^{2}}=\mathrm{Re}(S+\epsilon_{i(k)}T_i)$ with $\epsilon_{i(1)}=-\epsilon_{i(2)}$, where the normalization is fixed by axionic couplings from the 11D $C\wedge G\wedge G$ term, and that nonstandard embeddings allow mixing of gauge sectors across walls, yielding anomalous $U(1)_A$ cancelled by a Green–Schwarz mechanism. The work analyzes axionic threshold corrections, the role of zero and nonzero Calabi–Yau modes, and distinguishes two phenomenological regimes: a weaker observable sector with a potential critical radius and a stronger observable sector permitting near- or full-scale unification, each with implications for gaugino condensation and SUSY breaking. Overall, the study broadens the landscape of M-theory phenomenology by providing a concrete framework for realistic 4D models with mixed-wall gauge sectors, anomalous U(1)’s, and tunable gauge-coupling hierarchies.

Abstract

In this paper we discuss compactifications of M-theory to four dimensions on X \times S^1/Z_2, in which nonstandard embeddings in the E_8 \times E_8 vacuum gauge bundle are considered. At the level of the effective field theory description of Horava and Witten, this provides a natural extension of well known results at weak coupling, to strongly coupled E_8 \times E_8 heterotic strings. As an application of our results, we discuss models which exhibit an anomalous U(1)_A symmetry in four dimensions, and show how this emerges from the reduction of the d = 11 toplogical term C \wedge G \wedge G, and how it is consistent with d = 4 anomaly cancellation in M-theory. As a further application of nonstandard embeddings, we show how it is possible to obtain an inverse hierarchy of gauge couplings, where the observable sector is more strongly coupled than the hidden one. The basic construction and phenomenological viability of these scenarios is demonstrated.