Scale, Gauge Couplings, Soft Terms and Toy Compactification in M-theory on $S^1/Z_2$

TL;DR

This paper investigates the effects of higher-order corrections on scale, gauge couplings, and soft terms in M-theory compactifications on $S^1/Z_2$, proposing new relations and toy models to understand phenomenological implications.

Contribution

It introduces the importance of next-order corrections in M-theory compactifications and constructs toy models to analyze their impact on physical parameters.

Findings

Higher order terms significantly affect soft terms and gauge couplings.

Derived new relations for soft terms in standard and non-standard embeddings.

Showed that the Calabi-Yau volume cannot be pushed to zero along the eleventh dimension.

Abstract

In M-theory on $S^1/Z_2$, we point out that to be consistant, we should keep the scale, gauge couplings and soft terms at next order, and obtain the soft term relations: $M_{1/2} = -A$, $|{{M_{0}}/{M_{1/2}}}| \leq {1/{\sqrt 3}}$ in the standard embedding and $M_{1/2}=-A$ in the non-standard embedding with five branes and $K_{5,n}=0$. We construct a toy compactification model which includes higher order terms in 4-dimensional Lagrangian in standard embedding, and discuss its scale, gauge couplings, soft terms, and show that the higher order terms do affect the scale, gauge couplings and especially the soft terms if the next order correction was not small. We also construct a toy compactification model in non-standard embedding with five branes and discuss its phenomenology. We argue that one might not push the physical Calabi-Yau manifold's volume to zero at any point along the eleventh dimension.