Spinning squashed extra dimensions and chiral gauge theory from $\cal{N}=4$ SYM

TL;DR

This paper explores novel spinning solutions in $ ext{SU}(N)$ ${ m extbf{N=4}}$ SYM that produce a low-energy chiral fermion sector resembling the standard model, with potential implications for understanding extra dimensions and symmetry breaking.

Contribution

It introduces spinning self-intersecting extra dimension solutions in ${ m extbf{N=4}}$ SYM that generate chiral fermions and scalar fields, offering a new approach to model building.

Findings

Low-energy sector contains 3 generations of chiral fermions.

Localized zero modes are unaffected by background rotation.

Presence of tachyonic excitations suggests possible stabilization mechanisms.

Abstract

New solutions of $SU(N)$ ${\cal N}=4$ SYM on $\mathbb{R}^4$ interpreted as spinning self-intersecting extra dimensions are discussed. Remarkably, these backgrounds lead to a low-energy sector with 3 generations of chiral fermions coupled to scalar and gauge fields, with standard Lorentz-invariant kinematics. This sector arises from zero modes localized on the rotation axes, which are oblivious to the background rotation. The remaining modes are not described by a Lorentz-invariant field theory and are mostly "heavy", but there is one sextet of tachyonic excitations. Assuming that the latter get stabilized e.g. by quantum effects, we argue that different rotation frequencies would induce a VEV for some of the low-energy scalar fields. We discuss configurations which may lead to a low-energy physics not far from the broken phase of the standard model.