Orbifolds, fuzzy spheres and chiral fermions

TL;DR

This paper constructs chiral, anomaly-free gauge theories from orbifold projections of N=4 SYM, revealing vacua as fuzzy spheres and exploring their phenomenological implications, including spontaneous symmetry breaking to the MSSM.

Contribution

It introduces a novel method to generate chiral, anomaly-free models with fuzzy sphere vacua from orbifolded N=4 SYM, with potential phenomenological applications.

Findings

Identification of vacua as spontaneously generated fuzzy spheres.

Demonstration of gauge symmetry breaking to phenomenologically relevant groups.

Potential for models to be finite and to break to the MSSM without extra superfields.

Abstract

Starting with a N=4 supersymmetric Yang-Mills theory in four dimensions with gauge group SU(3N) we perform an orbifold projection leading to a N=1 supersymmetric SU(N)^3 Yang-Mills theory with matter supermultiplets in bifundamental representations of the gauge group, which is chiral and anomaly free. Subsequently, we search for vacua of the projected theory which can be interpreted as spontaneously generated twisted fuzzy spheres. We show that by adding the appropriate soft supersymmetry breaking terms we can indeed reveal such vacua. Three cases are studied, where the gauge group is spontaneously broken further to the low-energy gauge groups SU(4)xSU(2)xSU(2), SU(4)^3 and SU(3)^3. Such models behave in intermediate scales as higher-dimensional theories with a finite Kaluza-Klein tower, while their low-energy physics is governed by the corresponding zero-modes and exhibit chirality in the fermionic sector. The most interesting case from the phenomenological point of view turns out to be the SU(3)^3 unified theory, which has several interesting features such as (i) it can be promoted to a finite theory, (ii) it breaks further spontaneously first to the MSSM and then to SU(3)xU(1)_{em} due to its own scalar sector, i.e. without the need of additional superfields and (iii) the corresponding vacua lead to spontaneously generated fuzzy spheres.