Axion Shift Symmetry Research Articles

On the oscillating electric dipole moment induced by axion-fermion couplings

It has been recently claimed that the axion coupling to fermions is responsible for an oscillating electric dipole moment (EDM) in the background of axion dark matter. In this work, we re-examine the derivation of this effect. Contrary to previous studies, we point out the physical relevance of an axion boundary term, which is crucial in restoring the axion shift symmetry and drastically affects the EDM phenomenology. To describe the latter, we introduce the notion of a time-averaged effective axion EDM, which encodes the boundary term and whose magnitude depends on the oscillation regime. For slow oscillations, the boundary term washes out the standard oscillating EDM, resulting in an exact cancellation in the static limit. Conversely, during fast oscillations, the boundary term amplifies the effective EDM relatively to the standard EDM contribution. This observable is especially interesting in the case of the electron EDM. For an O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(1) axion-electron coupling, the overall size of the effective EDM in the regime of intermediate or fast oscillations is comparable to the present static EDM limit.

Coupling a Cosmic String to a TQFT

A common framework of particle physics consists of two sectors of particles, such as the Standard Model and a dark sector, with some interaction between them. In this work, we initiate the study of a qualitatively different setup in which one of the sectors is a topological quantum field theory (TQFT). Instead of particles, the physics of a TQFT only manifests itself in non-trivial spacetime topologies or in the presence of topological defects. In particular, we consider two possible ways in which axionic cosmic strings can interact with a ℤn TQFT. One of them, by extending the structure of the axion coupling, leads to specific predictions for the localized degrees of freedom on the cosmic string, which can in turn effect their evolution and leave observable signals. The second approach, by gauging a discrete subgroup of the axionic shift symmetry, leads to dramatic changes in the string spectrum. We stress that the scenario considered here should be regarded as a plausible way for new physics to arise since it can be the low energy effective field theory for quite generic scenarios at high energies. To demonstrate this point and further illustrate the physical implications, we construct UV completions for both of the cases of couplings to TQFTs. While detailed predictions for observable signals of such scenarios require further investigation, our results demonstrate that there are rich new phenomena in this scenario.

Axion-assisted resonance oscillation rescues the Dodelson–Widrow mechanism

The keV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{keV}$$\\end{document} scale sterile neutrino was a qualified candidate for dark matter particles in the Dodelson-Widrow mechanism. But the mixing angle, needed to provide enough amount of dark matter, is in contradiction with the astrophysical observations. To alleviate such tension, we introduce an effective interaction, i.e. ga(ϕ/Λ)∂μaνα¯γμγ5να\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_a (\\phi /\\Lambda )\\partial _{\\mu }a \\overline{\ u _\\alpha }\\gamma ^{\\mu } \\gamma _5 \ u _\\alpha $$\\end{document}, among Standard Model neutrino να\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u _\\alpha $$\\end{document}, axion a, and singlet ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document}. The axial-vector interaction form is determined by the axion shift symmetry, and the singlet ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} with dynamically varied vacuum expectation value is introduced to reinforce the axial-vector coupling strength and evade the stringent neutrino oscillation constraints. The effective potential generated by the new interaction could cancel the SM counterpart, resulting in an enhanced converting probability between SM neutrino and sterile neutrino. Hence, the production rate of sterile neutrinos can be substantially enlarged with smaller mixing compared to the DW mechanism.

Shift-Invariant Orders of an Axionlike Particle.

It is generally believed that global symmetries, in particular, axion shift symmetries, can only be approximate. This motivates one to quantify the breaking of the shift invariance that characterizes the flavorful effective couplings of an axionlike particle to standard model fermions. We identify a minimal set of Jarlskog-like flavor invariants that vanish if and only if the axion is shift symmetric. Therefore, they represent order parameters for the breaking of the axion shift symmetry. We illustrate properties of the invariants by matching to a UV model, studying the CP transformation of the invariants, calculating their renormalization group evolution, and investigating similar conditions in the low-energy effective field theory below the electroweak scale. Finally, we discuss the order parameter associated to the nonperturbative shift-breaking induced by the axion-gluons coupling, which is also flavorful.

Axion quality straight from the GUT

Composite axion scenarios offer a robust field theoretic justification for the existence of a Peccei–Quinn symmetry of high quality. We present a new class of realizations that are naturally embedded in Grand-Unified Theories, retain asymptotic freedom for all gauge groups, and protect the axion shift symmetry up to operators of dimension 12. Our setup leads to a number of distinctive signatures at low energies. First, additional composite scalars are predicted; some of these are viable dark matter candidates for values of the decay constant that are likely too low for the QCD axion abundance to be relevant. Second, an approximate unification of the Standard Model gauge couplings takes place at the axion scale, while leaving the actual quark-lepton unification at much higher energies as usual. This suggests the existence of GUT relics with Standard Model gauge quantum numbers at potentially accessible scales.

Axion induced spin effective couplings

Detecting axionic dark matter induced electron or nucleon oscillating electric dipole moment (OEDM) has become a new way for dark matter searches. We re-examine such axion-spin couplings in external electromagnetic fields. We point out that axion-photon interaction induces an electron spin effective coupling, which is different from an OEDM. In particular, the axion-spin effective coupling is directly related to magnetic field rather than electric field. For axion-electron or axion-nucleon couplings, an OEDM of fermion is introduced, whose effect in ultralight axion cases depends on whether axion shift symmetry is manifest. Specifically, ultralight axionic dark matter interactions that do not obey the shift symmetry will be strongly constrained. We also extend the results to the case where axion has a finite velocity.

Axion Kinetic Misalignment Mechanism.

In the conventional misalignment mechanism, the axion field has a constant initial field value in the early Universe and later begins to oscillate. We present an alternative scenario where the axion field has a nonzero initial velocity, allowing an axion decay constant much below the conventional prediction from axion dark matter. This axion velocity can be generated from explicit breaking of the axion shift symmetry in the early Universe, which may occur as this symmetry is approximate.

New K\xe4hler invariant Fayet\u2013Iliopoulos terms in supergravity and cosmological applications

Recently, a new type of constant Fayet–Iliopoulos (FI) terms was introduced in {mathcal {N}}=1 supergravity, which do not require the gauging of the R-symmetry. We revisit and generalise these constructions, building a new class of Kähler invariant FI terms parametrised by a function of the gravitino mass as functional of the chiral superfields, which is then used to describe new models of inflation. They are based on a no-scale supergravity model of the inflaton chiral multiplet, supplemented by an abelian vector multiplet with the new FI-term. We show that the inflaton potential is compatible with the CMB observational data, with a vacuum energy at the minimum that can be tuned to a tiny positive value. Finally, the axionic shift symmetry can be gauged by the U(1) which becomes massive. These models offer a mechanism for fixing the gravitino mass in no-scale supergravities, that corresponds to a flat direction of the scalar potential in the absence of the new FI-term; its origin in string theory is an interesting open problem.

Cosmological window onto the string axiverse and the supersymmetry breaking scale

In the simplest picture, the masses of string axions populating the axiverse depend on two parameters: the supersymmetry breaking scale $M_{\rm susy}$ and the action $S$ of the string instantons responsible for breaking the axion shift symmetry. In this work, we explore whether cosmological data can be used to probe these two parameters. Adopting string-inspired flat priors on $\log_{10}M_{\rm susy}$ and $S$, and imposing that $M_{\rm susy}$ be sub-Planckian, we find $S=198\pm28$. These bounds suggest that cosmological data complemented with string-inspired priors select a quite narrow axion mass range within the axiverse, $\log_{10}(m_a/{\rm eV}) = -21.5^{+1.3}_{-2.3}$. We find that $M_{\rm susy}$ remains unconstrained due to a fundamental parameter degeneracy with $S$. We explore the significant impact of other choices of priors on the results, and we comment on similar findings in recent previous literature.

The photophobic ALP

We explore models and phenomenology of a photophobic axion-like particle (ALP), an axion whose coupling to photons is maximally suppressed without fine-tuning of the underlying parameters. We demonstrate that photophobia can be a natural UV property of ALP models and determine the irreducible coupling of photophobic ALPs to photons induced by violations of the axion shift symmetry. The signatures of photophobic axions are radically different from those of typical ALPs and are of particular interest for collider-based experiments, for which Standard Model triboson measurements provide a significant probe at higher masses. A variety of terrestrial and astrophysical measurements constrain the parameter space of photophobic ALPs, though bounds are typically much weaker compared to typical ALPs. We discuss implications for particle production relaxion models based on photophobic ALPs, finding that they are in mild tension with existing experimental constraints.

Field redefinitions and K\xe4hler potential in string theory at 1-loop

Field redefinitions at string 1-loop order are often required by supersymmetry, for instance in order to make the Kähler structure of the scalar kinetic terms manifest. We derive the general structure of the field redefinitions and the Kähler potential at string 1-loop order in a certain class of string theory models (4-dimensional toroidal type IIB orientifolds with mathcal{N} = 1 supersymmetry) and for a certain subsector of fields (untwisted Kähler moduli and the 4-dimensional dilaton). To do so we make use of supersymmetry, perturbative axionic shift symmetries and a particular ansatz for the form of the 1-loop corrections to the metric on the moduli space. Our results also show which terms in the low-energy effective action have to be calculated via concrete string amplitudes in order to fix the values of the coefficients (in the field redefinitions and the Kähler potential) that are left undetermined by our general analysis based on (super)symmetry.

Backreacted axion field ranges in string theory

String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter is unconstrained by tadpoles and can in principle lead to a parametrically enhanced effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement.

New potentials for string axion inflation

We propose a new type of axion inflation with complex structure moduli in the framework of type IIB superstring theory compactified on Calabi-Yau manifold. The inflaton is identified as the axion for the complex structure moduli whose potential is originating from instantonic corrections appearing through the period vector of mirror Calabi-Yau manifold. The axionic shift symmetry is broken down to the discrete one by the inclusion of instantonic correction and certain three-from fluxes. Our proposed inflation scenario is compatible with K\"ahler moduli stabilization. We also study a typical reheating temperature in the case of complex structure moduli inflation.

Relaxion monodromy and the Weak Gravity Conjecture

The recently proposed relaxion models require extremely large trans-Planckian axion excursions as well as a potential explicitly violating the axion shift symmetry. The latter property is however inconsistent with the axion periodicity, which corresponds to a gauged discrete shift symmetry. A way to make things consistent is to use monodromy, i.e. both the axion and the potential parameters transform under the discrete shift symmetry. The structure is better described in terms of a 3-form field $C_{\mu \nu \rho}$ coupling to the SM Higgs through its field strength $F_4$. The 4-form also couples linearly to the relaxion, in the Kaloper-Sorbo fashion. The extremely small relaxion-Higgs coupling arises in a see-saw fashion as $g\simeq F_4/f$, with $f$ being the axion decay constant. We discuss constraints on this type of constructions from membrane nucleation and the Weak Gravity Conjecture. The latter requires the existence of membranes, whose too fast nucleation could in principle drive the theory out of control, unless the cut-off scale is lowered. This allows to constrain relaxion models on purely theoretical grounds. We also discuss possible avenues to embed this structure into string theory.

R2 inflation from scale invariant supergravity and anomaly free superstrings with fluxes

The scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non-supersymmetric case the conformally coupled scalars belong to an manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the Kählerian space =. In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a symmetry. The anomaly is resolved via the gauging of a Peccei-Quinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always as a sub-manifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral (or even ) supersymmetric vacua via a Green-Schwarz/Peccei-Quinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the no-scale modulus.

A holomorphic anomaly in the elliptic genus

We consider a class of gauged linear sigma models (GLSMs) in two dimensions that flow to non-compact (2, 2) superconformal field theories in the infra-red, a prototype of which is the SL(2, ℝ)/U(1) (cigar) coset. We compute the elliptic genus of the GLSMs as a path-integral on the torus using supersymmetric localization. We find that the result is a Jacobi-like form that is non-holomorphic in the modular parameter τ of the torus, with mock modular behavior. This agrees with a previously-computed expression in the cigar coset. We show that the lack of holomorphicity of the elliptic genus arises from the contributions of a compact boson carrying momentum and winding excitations. This boson has an axionic shift symmetry and plays the role of a compensator field that is needed to cancel the chiral anomaly in the rest of the theory.

New Class ofN=1No-Scale Supergravity Models

We introduce a new N=1 no-scale supergravity model with F- and D-term breaking. It contains a single chiral supermultiplet T and a single U(1) vector multiplet U, gauging a nonanomalous axionic shift symmetry. Both supersymmetry and the gauge symmetry are spontaneously broken, with the spin-3/2, spin-1, and spin-1/2 masses sliding along a classical flat direction, with a single real massless scalar in the spectrum. The other degrees of freedom are absorbed by the massive gravitino and vector. We extend our model, under very mild conditions, to general gauge groups and matter content.

A Natural Framework for Chaotic Inflation

We show that inflation with a quadratic potential occurs naturally in theories where an axionlike field mixes with a 4-form. Such an axion is massive, with the mass which arises from the mixing being protected by the axion shift symmetry. The 4-form backgrounds break this symmetry spontaneously and comprise a minilandscape, where their fluxes can change by emission of membranes. Inflation can begin when the 4-form dominates the energy density. Eventually, this energy is reduced by membrane emission, and the axion can roll slowly towards its minimum, as in the simplest version of chaotic inflation.

Where in the string landscape is quintessence?

We argue that quintessence may reside in certain corners of the string landscape. It arises as a linear combination of internal space components of higher-rank forms, which are axionlike at low energies, and may mix with 4-forms after compactification of the Chern-Simons terms to 4D due to internal space fluxes. The mixing induces an effective mass term, with an action which preserves the axion shift symmetry, breaking it spontaneously after the background selection. With several axions, several 4-forms, and a low string scale, as in one of the setups already invoked for dynamically explaining a tiny residual vacuum energy in string theory, the 4D mass matrix generated by random fluxes may have ultralight eigenmodes over the landscape, which are quintessence. We illustrate how this works in the simplest cases, and outline how to get the lightest mass to be comparable to the Hubble scale now, ${H}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}33}\text{ }\text{ }\mathrm{eV}$. The shift symmetry protects the smallest mass from perturbative corrections in field theory. Further, if the ultralight eigenmode does not couple directly to any sector strongly coupled at a high scale, the nonperturbative field theory corrections to its potential will also be suppressed. Finally, if the compactification length is larger than the string length by more than an order of magnitude, the gravitational corrections may remain small too, even when the field value approaches ${M}_{\mathrm{Pl}}$.

Quantum lift of non-BPS flat directions

We study N = 2 , d = 4 attractor equations for the quantum corrected two-moduli prepotential F = s t 2 + i λ , with λ real, which is the only correction which preserves the axion shift symmetry and modifies the geometry. In the classical case the black hole effective potential is known to have a flat direction. We found that in the presence of D 0 – D 6 branes the black hole potential exhibits a flat direction in the quantum case as well. It corresponds to non-BPS Z ≠ 0 solutions to the attractor equations. Unlike the classical case, the solutions acquire non-zero values of the axion field. For the cases of D 0 – D 4 and D 2 – D 6 branes the classical flat direction reduces to separate critical points which turn out to have a vanishing axion field.