Dirac operator spectrum on a nilmanifold

TL;DR

This paper computes the Dirac operator spectrum on a specific nilmanifold and explores its dependence on geometric parameters, then applies these results to derive a 4D effective theory from a 7D gauge-fermion model.

Contribution

It provides the explicit spectrum of the Dirac operator on the Heisenberg nilmanifold and connects it to low-energy effective actions in four dimensions.

Findings

Spectrum explicitly depends on metric moduli.

Complete characterization of Dirac spectrum on $ ext{Heisenberg}$ nilmanifold.

Derived 4D effective action from 7D gauge-fermion theory.

Abstract

We obtain the spectrum of the Dirac operator on the three-dimensional Heisenberg nilmanifold $\mathcal{M}_3$, and its complete dependence on the metric moduli. As an application, we construct the four-dimensional low-energy effective action obtained by compactification of a seven-dimensional gauge-fermion theory on $\mathcal{M}_3$.