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We show that axions interacting with abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both nonabelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential vanishes in the presence of a massless charged fermion and that it is robust against the presence of higher-derivative corrections in the effective Lagrangian. Finally, as a first step toward connecting with particle phenomenology and cosmology, we discuss the regime in which this potential is important in determining the dark matter relic abundance in a hidden sector containing an abelian gauge group, monopoles, and axions.
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We calculate a new contribution to the axion mass that arises from gluons propagating in a 5th dimension at high energies. By uplifting the 4D instanton solution to five dimensions, the positive frequency modes of the Kaluza-Klein states generate a power-law term in the effective action that inversely grows with the instanton size. This causes 5D small instantons to enhance the axion mass in a way that does not spoil the axion solution to the strong CP problem. Moreover this enhancement can be much larger than the usual QCD contribution from large instantons, although it requires the 5D gauge theory to be near the non-perturbative limit. Thus our result suggests that the mass range of axions (or axion-like particles), which is important for ongoing experimental searches, can depend sensitively on the UV modification of QCD.
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Various theoretical and experimental considerations motivate models with high scale supersymmetry breaking. While such models may be difficult to test in colliders, we propose looking for signatures at much lower energies. We show that a keV line in the X-ray spectrum of galaxy clusters (such as the recently disputed 3.5 keV observation) can have its origin in a universal string axion coupled to a hidden supersymmetry breaking sector. A linear combination of the string axion and an additional axion in the hidden sector remains light, obtaining a mass of order 10 keV through supersymmetry breaking dynamics. In order to explain the X-ray line, the scale of supersymmetry breaking must be about $10^{11-12}$ GeV. This motivates high scale supersymmetry as in pure gravity mediation or minimal split supersymmetry and is consistent with all current limits. Since the axion mass is controlled by a dynamical mass scale, this mass can be much higher during inflation, avoiding isocurvature (and domain wall) problems associated with high scale inflation. In an appendix we present a mechanism for dilaton stabilization that additionally leads to $mathcal{O}(1)$ modifications of the gaugino mass from anomaly mediation.
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