On the chirality of the SM and the fermion content of GUTs

TL;DR

This paper investigates the constraints on fermion content in GUTs imposed by the chirality of the Standard Model, exploring non-standard fermion representations and their decompositions to achieve correct SM chirality.

Contribution

It systematically analyzes non-standard fermion GUT representations that can reproduce the Standard Model's chirality, expanding beyond traditional arrangements.

Findings

Certain large GUT representations can yield SM-like chirality

Non-standard fermion mixtures are possible for family unification

Decomposition patterns of GUT representations can match SM fermion content

Abstract

The Standard Model (SM) is a chiral theory, where right- and left-handed fermion fields transform differently under the gauge group. Extra fermions, if they do exist, need to be heavy otherwise they would have already been observed. With no complex mechanisms at work, such as confining interactions or extra-dimensions, this can only be achieved if every extra right-handed fermion comes paired with a left-handed one transforming in the same way under the Standard Model gauge group, otherwise the new states would only get a mass after electroweak symmetry breaking, which would necessarily be small ($\sim100\textrm{ GeV}$). Such a simple requirement severely constrains the fermion content of Grand Unified Theories (GUTs). It is known for example that three copies of the representations $\mathbf{\overline{5}}+\mathbf{10}$ of $SU(5)$ or three copies of the $\mathbf{16}$ of $SO(10)$ can reproduce the Standard Model's chirality, but how unique are these arrangements? In a systematic way, this paper looks at the possibility of having non-standard mixtures of fermion GUT representations yielding the correct Standard Model chirality. Family unification is possible with large special unitary groups --- for example, the $\mathbf{171}$ representation of $SU(19)$ may decompose as $3\left(\mathbf{16}\right)+\mathbf{120}+3\left(\mathbf{1}\right)$ under $SO(10)$.