Axion couplings in Orbifold GUTs

TL;DR

The paper analyzes how axions couple to gauge bosons in orbifold GUTs inspired by string constructions, showing that axion–gauge couplings are topological and fixed by the SM embedding in the UV group. It distinguishes bulk higher-form axions, which couple in a GUT-symmetric way, from brane-localised axions, which can couple to photons independently of QCD but acquire large masses from UV instantons under apparent unification; mixing can yield higher-axions with universal couplings. Under the requirement of approximate gauge coupling unification, all photon-coupled axions satisfy the bound $\frac{g_{a\gamma\gamma}}{m_a}$ not exceeding the QCD axion line, implying the QCD axion in these models lies near the conventional neV mass range, with heavier ALPs appearing as a cosmologically interesting but experimentally challenging sector. The work connects 5D orbifold GUTs to dimensional deconstruction and type-II string setups, offering a UV-complete perspective on axion phenomenology and guiding experimental targets for QCD axion searches versus heavier ALPs.

Abstract

We consider the coupling of axions to gauge bosons in higher-dimensional Grand Unified Theories (GUT) inspired by string theory constructions with D-branes on orbifold singularities, the so-called orbifold GUTs. Due to their topological properties, axion couplings to gauge bosons are independent of the gauge symmetry reduction mechanism and the background geometry -- they only depend on the embedding of the SM into the UV gauge group. There are two kinds of axions in this class of theories: axions coming from gauge fields in the bulk and axions localised on the boundaries. The axion-photon coupling for the bulk axions coincide with the results from 4-dimensional GUTs, where axions which couple to photons necessarily couple also to QCD. The brane-localised axions can couple to photons independently of the QCD coupling, but if gauge couplings are approximately unified, the axions get large masses from unsuppressed instantons on the boundaries. This means that the ratio $g_{aγγ}/m_a$ is below (or equal to) the QCD axion value for all axions in orbifold GUTs, as is the case for unified theories in 4d.

Figures (3)

• Figure 1: Preditions for $g_{a\gamma\gamma}$ and $m_a$ for the QCD axion (solid black) as well as brane-localised ALPs (dashed lines) with different choices of the relevant parameters according to the benchmarks in Table \ref{['tab:results']}. Purple corresponds to low KK scale $l_5^{-1}\sim 10^9$ GeV and large chiral suppression, $K=5\times 10^{-13}$. Orange corresponds to low KK scale and no chiral suppression, $K=1$. Dark green corresponds to a model with large KK scale, $l_5^{-1}\sim 10^{16}$ GeV and $K=5\times 10^{-13}$. All cases assume $\Delta\alpha^{-1}=3$. The dark red region, corresponding to the parameter space where \ref{['eq:coupling-to-mass_ratio']} is violated, is not accessible to orbifold GUTs with apparent unification. Experimental bounds adapted from AxionLimits.
• Figure 2: Deconstructed orbifold GUT. Each site has a $SU(5)$ gauge sector which is Higgsed down to the diagonal subgroup via the vev of bi-fundamental (link) fields, $\Sigma_i$. The last boundary site, in red, contains a $SU(3)\times SU(2)\times U(1)$ gauge sector which is physically relevant (not an artifact from the deconstruction picture). It may contain fields transforming in SM representations that do not fill out a full $SU(5)$ multiplet. This site can also contain axion-like particles which couple to gauge bosons in a non GUT-symmetric way. As explained in the text these ALPs get a large mass due to non-perturbative effects with a small instanton action. The action can be calculated by using the UV gauge coupling $S_{i}\sim \frac{2\pi}{\alpha_i}$, with $\alpha_i$ the localised gauge coupling.
• Figure 3: Diagram showing the D-7 brane setup which gives an analogue of the orbifold GUT model. The stack of branes which form the bulk span the $y_{1 - 4}$ directions, while the boundary branes are extended in the $y_{3 -6}$ directions. The intersection of the branes is indicated by the shaded regions, which extend in the directions $y_{3, 4}$. The 5d theory is obtained by integrating over the co-ordinates $y_3 - y_6$ and one of $y_1, y_2$.