Pseudo-Nambu-Goldstone bosons and tachyons in flux compactification

TL;DR

This paper investigates how flux compactification in higher-dimensional gauge theories leads to pseudo-Nambu-Goldstone bosons with finite, protected masses and explores conditions under which tachyonic modes can be eliminated in $SU(2)$ models.

Contribution

It demonstrates the emergence of pseudo-Nambu-Goldstone bosons with stable masses and provides a mechanism to remove tachyons in $SU(2)$ gauge theories via scalar VEVs and coupling adjustments.

Findings

Pseudo-Nambu-Goldstone bosons have finite, quantum-corrected masses.

Tachyonic modes can be eliminated in $SU(2)$ models with large coupling constants.

Scalar VEVs can preserve fermion chirality while removing tachyons.

Abstract

In a six-dimensional gauge theory compactified on a torus with magnetic flux, translational symmetry in the extra dimensions is broken. As a result, a massless Nambu-Goldstone boson appears in the four-dimensional effective Lagrangian. We show that a model with two $U(1)$ gauge symmetries includes a pseudo-Nambu-Goldstone scalar boson, whose mass is finite but shielded from large quantum corrections. This opens the door to achieving scalar masses in the TeV range. Additionally, we explore the presence of tachyons in the effective Lagrangian for $SU(2)$ gauge theories. By introducing a scalar field in the adjoint representation of $SU(2)$ with a finite vacuum expectation value, we demonstrate that tachyonic modes can be eliminated for sufficiently large values of the coupling constant, while preserving fermion chirality in the model.