Standard Model Vacua for Two-dimensional Compactifications

TL;DR

This paper explores two-dimensional compactifications of the standard model on different surfaces, discovering a new vacuum on a torus influenced by quantum effects, and analyzing conditions for stable vacua on spheres.

Contribution

It identifies a new standard model vacuum on a 2D torus influenced by quantum effects and clarifies conditions for stable vacua on spheres with magnetic flux.

Findings

A new standard model vacuum exists on a 2D torus for a range of neutrino masses.

Quantum effects are essential for the existence of the torus vacuum.

Stable vacua on a sphere require large magnetic flux; no vacua are found for higher genus surfaces.

Abstract

We examine the structure of lower-dimensional standard model vacua for two-dimensional compactifications (on a 2D torus and on a 2D sphere). In the case of the torus we find a new standard model vacuum for a large range of neutrino masses consistent with experiment. Quantum effects play a crucial role in the existence of this vacuum. For the compactification on a sphere the classical terms dominate the effective potential for large radii and a stable vacuum is achieved only by introducing a large magnetic flux. We argue that there are no two-dimensional standard model vacua for compactifications on a surface of genus greater than one.