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.
Quantum gravity introduces a new source of the combined parity (CP) violation in gauge theories. We argue that this new CP violation gets bundled with the strong CP violation through the coloured gravitational instantons. Consequently, the standard axion solution to the strong CP problem is compromised. Further, we argue that the ultimate solution to the strong CP problem must involve at least one additional axion particle.
We examine the contribution of small instantons to the axion mass in various UV completions of QCD. We show that the reason behind the potential dominance of such contributions is the non-trivial embedding of QCD into the UV theory. The effects from instantons in the partially broken gauge group appear as "fractional instanton" corrections in the effective theory. These will exhibit unusual dependences on the various scales in the problem whenever the index of embedding is non-trivial. We present a full one-instanton calculation of the axion mass in the simplest product group models, carefully…
We investigate the axion inflation model derived by poly-instanton effects in type II superstring theories. Poly-instanton effects are instanton effects corrected by another instanton and it can generate the modulus-axion potential with the double exponential function. Although the axion has a period of small value, this potential can have a flat region because its derivatives are exponentially suppressed by non-perturbative effects. From the view point of the cosmic inflation, such potential is interesting. In this paper, we numerically study the possibilities for realizing the cosmic inflati…
We investigate the role of gauge and gravitational instantons in the context of the Swampland program. Our focus is on the global symmetry breaking they induce, especially in the presence of fermions. We first recall and make more precise the description of the dilute instanton gas through a 3-form gauge theory. In this language, the familiar suppression of instanton effects by light fermions can be understood as the decoupling of the 3-form. Even if all fermions remain massive, such decoupling may occur on the basis of an explicitly unbroken but anomalous global symmetry in the fermionic sect…
Small size QCD instantons may spoil the axion solution to the strong CP problem if QCD is not asymptotically free at high energy scales. We examine this issue in supersymmetric models using a manifestly supersymmetric scheme to compute the axion potential induced by small size instantons. Applying this scheme for a class of illustrative models, it is found that the resulting high energy axion potential is highly model-dependent, but suppressed by more powers of the soft supersymmetry breaking parameters and/or of the other small mass scales than what is expected based on a naive instanton grap…
We construct a new framework to calculate the enhancement of axion masses and concomitant effects on axion-meson mixing arising from small size instantons (SSIs), which originate in models featuring an extended color gauge symmetry. The framework is based on an explicit evaluation of 't Hooft determinantal operators that partition into instanton amplitudes, affording a more precise determination of the axion-diphoton coupling than previous results. Using an explicit model first presented in Ref. arXiv:1805.06465, we demonstrate that axions solving the strong CP problem can have electroweak sca…
The axion mass receives a large correction from small instantons if the QCD gets strongly coupled at high energies. We discuss the size of the new CP violating phases caused by the fact that the small instantons are sensitive to the UV physics. We also discuss the effects of the mass correction on the axion abundance of the Universe. Taking the small-instanton contributions into account, we propose a natural scenario of axion dark matter where the axion decay constant is as large as $10^{15\text{-}16}$GeV. The scenario works in the high-scale inflation models.
We present a new mechanism to relax the initial misalignment angle of the QCD axion and raise the cosmological bound on the axion decay constant. The QCD axion receives a contribution from small UV instantons during inflation, which raises its mass to the inflationary Hubble scale. This makes the axion start rolling down its potential early on. In the scenario, the standard model Yukawa couplings of quarks are dynamical, being of order one during the inflationary era and reducing to their standard model values once it ends. This means that after inflation the contribution of the small instanto…
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 v…
We show that a new chiral, confining interaction can be used to break Peccei-Quinn symmetry dynamically and solve the domain wall problem, simultaneously. The resulting theory is an invisible QCD axion model without domain walls. No dangerous heavy relics appear.
We show that QCD instantons can generate large effects at small length scales in the ultraviolet in standard composite Higgs models that utilise partial compositeness. This has important implications for possible solutions of the strong CP problem in these models. First we show that in the simplest known UV completions of composite Higgs models, if an axion is also present, it can have a mass much larger than the usual QCD axion. Even more remarkable is the case where there are no axions, but the strong CP problem can be solved by generating the up quark mass entirely from the contribution of …
Recent cosmological observations suggest the presence of small but nonzero cosmological constant $Λ_{cos}^4 \simeq (2 \times 10^{-3} eV)^4$. It is an intriguing possibility that such a small cosmological constant is supplied by the potential energy density of an ultralight axion-like field (called as quintessence axion). If this axion couples to the electroweak gauge fields, its potential may be generated by the electroweak instanton effects. We calculate the axion potential assuming the supersymmetric standard model and obtain a surprising result that the induced energy density of the quintes…
We discuss quantum gravitational effects in Einstein theory coupled to periodic axion scalars to analyze the viability of several proposals to achieve superplanckian axion periods (aka decay constants) and their possible application to large field inflation models. The effects we study correspond to the nucleation of euclidean gravitational instantons charged under the axion, and our results are essentially compatible with (but independent of) the Weak Gravity Conjecture, as follows: Single axion theories with superplanckian periods contain gravitational instantons inducing sizable higher harm…
If there is explicit violation of baryon plus lepton number at some energy scale, then the electroweak theory depends upon a θ-angle. Due to a singular integration over small scale size instantons, this θ-dependence is sensitive to very high momentum scales. Assuming that there is no new physics between the electroweak and Planck scales, for an electroweak axion the energy difference between the vacuum at θ /= 0, and that at θ = 0, is of the correct order of magnitude to be the dark energy observed in the present epoch.
Supersymmetric Peccei-Quinn symmetry and string theory predict a complex scalar field comprising a dilaton and an axion. These fields are massless at high energies, but it is known since long that the axion is stabilized in an instanton dominated vacuum. Instantons and axions together also provide a mechanism to stabilize a dilaton, thus accounting for a dilaton as a possible cold dark matter component accompanying the axion. We briefly review the prospects of this scenario and point out further implications.
Assuming QCD exhibits an interacting fixed-point behaviour in the ultraviolet regime, I argue that the axion can be substantially heavier than in the conventional case of asymptotically free QCD due to the enhanced contribution of small size instantons to its mass.
If the QCD axion is a significant component of dark matter, and if the universe was once hotter than a few hundred MeV, the axion relic abundance depends on the function $χ(T)$, the temperature-dependent topological susceptibility. Uncertainties in this quantity induce uncertainties in the axion mass as a function of the relic density, or vice versa. At high temperatures, theoretical uncertainties enter through the dilute instanton gas computation, while in the intermediate and strong coupling regime, only lattice QCD can determine $χ(T)$ precisely. We reassess the uncertainty on the instanton…
We study possibilities for lowering the decay constants of superstring axions. In the heterotic Calabi-Yau compactification, a localized model-dependent axion can appear at a nearly collapsing 2-cycle. The effect of flux can be used for generating warp factor suppression of the axion decay constant. We also point out that the hidden sector instanton potential much higher than the QCD instanton potential picks up the larger effective axion decay constant as that of the QCD axion. We show that this can be converted by introducing many hidden-sector quarks so that the decay constant of the QCD ax…
Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility $χ(T)$ of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine $χ(T)$ in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are…
We study cosmological solutions in the context of 4-dimensional low energy Heterotic M-theory with moving bulk branes. In particular we present non-trivial, analytic axion solutions generated by new symmetries of the full potential-free action which are similar to 'triple axion' solutions found in Pre-Big-Bang (PBB) cosmologies. We also consider the presence of a non-perturbative superpotential, for which we find cosmological solutions with and without a background perfect fluid. In the absence of a fluid the dilaton and the T-modulus go to the potential-free solutions at late time, while the …
We show that models in which the strong $CP$ problem is solved by introducing an axion field with a mass enhanced by non-QCD UV dynamics at a scale $Λ_{\rm SI}$ exhibit enhanced sensitivity to external sources of $CP$ violation. In the presence of higher-dimensional $CP$-odd sources at a scale $Λ_{\rm CP}$, the same mechanisms that enhance the axion mass also modify the axion potential, shifting the potential minimum by a factor $\proptoΛ^2_{\rm SI}/Λ^2_{\rm CP}$. This phenomenon of $CP$-violation enhancement, which puts stringent constraints on the scale of new physics, is explicitly demonstr…
Any would-be Peccei-Quinn (PQ) symmetry is vulnerable to various types of explicit breaking. It has long been recognized that these can disrupt the axion solution to the strong CP problem. There have also been suggestions that, under certain circumstances, these can lead to a surprisingly large mass for the axion. Two types of corrections to this computation have been widely considered: higher dimension symmetry breaking operators, in theories where there is a complex field responsible for the spontaneous breaking of the PQ symmetry, and small instantons. Motivated by situations where small in…
This is the last in a series of papers on the topological susceptibility in the interacting instanton liquid model (IILM). We will derive improved finite temperature interactions to study the thermodynamic limit of grand canonical Monte Carlo simulations in the quenched and unquenched case with light, physical quark masses. In particular, we will be interested in chiral symmetry breaking. The paper culminates by giving, for the first time, a well-motivated temperature-dependent axion mass. Especially, this work finally provides a computation of the axion mass in the low temperature regime, $m^…
We study the phenomenology of the 'companion-axion model' consisting of two coupled QCD axions. The second axion is required to rescue the Peccei-Quinn solution to the strong-CP problem from the effects of colored gravitational instantons. We investigate here the combined phenomenology of axion-axion and axion-photon interactions, recasting present and future single-axion bounds onto the companion-axion parameter space. Most remarkably, we predict that future axion searches with haloscopes and helioscopes may well discover two QCD axions, perhaps even within the same experiment.
In a previous work, we analyzed collapsing axion stars using the low-energy instanton potential, showing that the total energy is always bounded and that collapsing axion stars do not form black holes. In this paper, we provide a proof that the conclusions are unchanged when using instead the more general chiral potential for QCD axions.
String theoretic axion is a prime candidate for the QCD axion solving the strong CP problem. For a successful realization of the QCD axion in string theory, one needs to stabilize moduli including the scalar partner (saxion) of the QCD axion, while keeping the QCD axion unfixed until the low energy QCD instanton effects are turned on. We note that a simple generalization of KKLT moduli stabilization provides such set-up realizing the axion solution to the strong CP problem. Although some details of moduli stabilization are different from the original KKLT scenario, this set-up leads to the mir…
This is the first in a series of papers which ultimately aims on improving on the present estimates on the axion mass by modeling the topological non-perturbative QCD dynamics. Axions couple to instantons and their mass is set by the topological susceptibility whose temperature dependence we estimate with the interacting instanton liquid model (IILM). Since accurate finite temperature instanton calculations have problems and do not consider fluctuations in the topological charge, we develop an improved grand canonical version of the IILM to study topological fluctuations in the quark gluon pla…
Dynamical mechanisms to generate an ultralight axion of mass $\sim 10^{-21}-10^{-22}$ eV in supergravity and strings are discussed. An ultralight particle of this mass provides a candidate for dark matter that may play a role for cosmology at scales $10\, {\rm kpc}$ or less. An effective operator approach for the axion mass provides a general framework for models of ultralight axions, and in one case recovers the scale $10^{-21}-10^{-22}$ eV as the electroweak scale times the square of the hierarchy with an $O(1)$ Wilson coefficient. We discuss several classes of models realizing this framewor…
The highly populated, low-energy excitations of a scalar field of mass $m_a\sim 10^{-22}\,\textrm{eV}$ can represent the full dark matter content of the universe and alleviate some tensions in the standard cosmological scenario on small-scales. This {\it fuzzy dark matter} component is commonly assumed to arise as the consequence of a new axion-like particle in the matter sector, yet for simplicity it is usually modeled in terms of a simple free quadratic field. In this paper we consider how the cosmological constraints are modified when the effects of an instanton potential and temperature-de…
We consider extensions of the standard model inspired by intersecting D-brane constructions, in order to address flavor mass textures. We include additional anomalous gauge symmetries, and scalar fields to break them and to generate Froggatt-Nielsen mass terms. Green-Schwarz axions are included to cancel mixed anomalies rendering the models consistent. At low energies, a residual anomalous global symmetry remains, and its associated pseudo-Goldstone mode becomes the physical axion, which can be interpreted as an axion arising from open string modes. General considerations show that such axions…
Taken individually, magnetic monopoles and axions are both well-motivated aspects of physics beyond the Standard Model. We demonstrate that by virtue of the Witten effect, their interplay is furthermore nontrivial; monopoles break the corresponding axial symmetries explicitly and result in an axion potential lacking the usual instanton-derived exponential suppression factor. As axions are distinguished by their extremely weak interactions, any regime where their effects are enhanced may be of interest. As an application of these findings, we demonstrate that a phenomenologically acceptable pop…
We discuss the idea that the model-independent (MI) axion of string theory is the source of quintessential dark energy. The scenario is completed with a composite QCD axion from hidden sector squark condensation that could serve as dark matter candidate. The mechanism relies on the fact that the hidden sector anomaly contribution to the composite axion is much smaller than the QCD anomaly term. This intuitively surprising scenario is based on the fact that below the hidden sector scale $Λ_h$ there are many light hidden sector quarks. Simply, by counting engineering dimensions the hidden sector…
The serious cosmological problems created by the axion-string/axion-domain-wall system in standard axion models are alleviated by positing the existence of a new confining force. The instantons of this force can generate an axion potential that erases the axion strings long before QCD effects become important, thus preventing QCD-generated axion walls from ever appearing. Axion walls generated by the new confining force would decay so early as not to contribute significantly to the energy in axion dark matter.
The axion solution to the strong CP problem is delicately sensitive to Peccei-Quinn breaking contributions that are misaligned with respect to QCD instantons. Heavy QCD axion models are appealing because they avoid this so-called "quality problem". We show that generic realizations of this framework can be probed by the LIGO-Virgo-KAGRA interferometers, through the stochastic gravitational wave (GW) signal sourced by the long-lived axionic string-domain wall network, and by upcoming measurements of the neutron and proton Electric Dipole Moments. Additionally, we provide predictions for searche…
We present the results on topological susceptibility and chiral observables in $N_f=2+1+1$ QCD for temperature range $120<T<600$ MeV. The lattice simulations are performed with Wilson twisted mass fermions at physical pion, strange and charm masses. In high-$T$ region $T\gtrsim 300$ MeV the chiral observables are shown to follow leading order Griffith analyticity, and the topological susceptibility follows a power-law decay as in the instanton dilute gas models. The measured topological susceptibility is used to estimate the mass of QCD axion. The resulting axion mass constraints are in agreem…
If a global chiral symmetry is explicitly broken by anomalies in nonabelian gauge theories, a pseudo Nambu-Goldstone boson (axion) associated with a spontaneous breakdown of such a global symmetry acquires a mass through nonperturbative instanton effects. We calculate the axion mass assuming a supersymmetric SU(2) gauge theory and show that the axion obtains an extremely small mass when the SU(2) gauge symmetry is broken down at very high energy, say at the Planck scale. We identify the axion with a hypothetical ultralight boson field proposed to account for a small but nonzero cosmological co…
We investigate the topological properties of $N_f = 2+1$ QCD with physical quark masses, both at zero and finite temperature. We adopt stout improved staggered fermions and explore a range of lattice spacings $a \sim 0.05 - 0.12$ fm. At zero temperature we estimate both finite size and finite cut-off effects, comparing our continuum extrapolated results for the topological susceptibility $χ$ with predictions from chiral perturbation theory. At finite temperature, we explore a region going from $T_c$ up to around $4\, T_c$, where we provide continuum extrapolated results for the topological sus…
1. Introduction 2. Models: the QCD axion; the strong CP problem; PQWW, KSVZ, DFSZ; anomalies, instantons and the potential; couplings; axions in string theory 3. Production and I.C.'s: SSB and non-perturbative physics; the axion field during inflation and PQ SSB; cosmological populations - decay of parent, topological defects, thermal production, vacuum realignment 4. The Cosmological Field: action; background evolution; misalignment for QCD axion and ALPs; cosmological perturbation theory - i.c.'s, early time treatment, axion sound speed and Jeans scale, transfer functions and WDM; the Schrod…
The temperature dependence of the topological susceptibility in QCD, chi_t, essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched a…
We consider heterotic string compactifications to four dimensions when instantons shrink to zero size. If the standard model gauge group originates from the new gauge symmetry associated with the small instantons singularity, then the weakly or strongly coupled heterotic string scales can be taken to be arbitrarily low. The SO(32) and E_8\times E_8 gauge groups can then be very weakly coupled even at the string scale and behave as non-abelian global symmetries. We comment on a possible role of small instantons in supersymmetry breaking.
Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to b…
We study instanton effects in theories with compact extra dimensions. We perform an instanton calculation in a 5d theory on a circle of radius R, with gauge, scalar, and fermion fields in the bulk of the extra dimension. We show that, depending on the matter content, instantons of size rho << R can dominate the amplitude. Using deconstruction as an ultraviolet definition of the theory allows us to show, in a controlled approximation, that for a small number of bulk fermions, the amplitude for small size instantons exponentially grows as e^{O(1)R/rho}.
