Natural Theories of Ultra-Low Mass PNGB's: Axions and Quintessence

TL;DR

The paper tackles the challenge of natural ultra-low mass PNGBs in the presence of Planck-scale symmetry breaking by embedding a lattice of $U(1)$ gauge groups into a deconstructed extra dimension. The Wilson Line PNGB arises as the zero mode of the fifth component $A_4$, with a nonlocal product of linking fields $\widetilde{\Phi}$ protecting it from gravity-induced operators; its mass and couplings are tunable via the lattice parameters, enabling both axion physics and quintessence. A minimal axion realization is achieved by embedding the SM in a $[U(1)_Y]^N$ theory and introducing bulk fermions to provide the anomalous coupling to $G\tilde{G}$, while Planck-scale corrections remain suppressed for $N\gtrsim 14$ and $f_a\sim 10^{12}$ GeV. The quintessence scenario is explored via the same WLPNGB framework, where Planck-scale effects can be controlled or even used to generate an ultra-light mass, with the Coleman–Weinberg potential arising as a finite, calculable contribution when fermions propagate in the bulk. Overall, the work provides a theory-space (deconstructed) mechanism to realize natural, ultra-light PNGBs with suppressed gravity-induced breaking, linking extra-dimensional geometry to axion and dark-energy phenomenology.

Abstract

We consider the Wilson Line PNGB which arises in a U(1)^N gauge theory, abstracted from a latticized, periodically compactified extra dimension U(1). Planck scale breaking of the PNGB's global symmetry is suppressed, providing natural candidates for the axion and quintessence. We construct an explicit model in which the axion may be viewed as the 5th component of the U(1)_Y gauge field in a 1+4 latticized periodically compactified extra dimension. We also construct a quintessence PNGB model where the ultra-low mass arises from Planck-scale suppressed physics itself.