Moduli Stabilisation in Heterotic Models with Standard Embedding

TL;DR

This paper investigates the challenges of stabilizing moduli in heterotic string compactifications with SU(3) structure, demonstrating that standard approaches face fundamental no-go theorems preventing Minkowski vacua.

Contribution

It provides a detailed analysis of moduli and matter field truncation effects and proves a no-go theorem based on flux constraints from the Bianchi identity.

Findings

Effective models lack satisfactory solutions.

Stabilized vacua are not achievable under the studied conditions.

A no-go theorem prevents Minkowski vacua in these models.

Abstract

In this note we analyse the issue of moduli stabilisation in 4d models obtained from heterotic string compactifications on manifolds with SU(3) structure with standard embedding. In order to deal with tractable models we first integrate out the massive fields. We argue that one can not only integrate out the moduli fields, but along the way one has to truncate also the corresponding matter fields. We show that the effective models obtained in this way do not have satisfactory solutions. We also look for stabilised vacua which take into account the presence of the matter fields. We argue that this also fails due to a no-go theorem for Minkowski vacua in the moduli sector which we prove in the end. The main ingredient for this no-go theorem is the constraint on the fluxes which comes from the Bianchi identity.