Axion fields provide the most elegant solution to the strong CP problem. In string compactifications it is difficult to obtain an axion whose decay constant is consistent with current cosmological bounds. We examine this question in theories with accidental U(1) symmetries that appear as low energy remnants of discrete symmetries. We refer to the axion-like particles from the spontaneous breakdown of these symmetries as accions. In such systems, the accion decay constant depends on the vacuum configuration and can be lowered to fit the bounds. Furthermore, we find that such accions with consistent decay constant can be embedded in special vacua of Z_6-II orbifold models with realistic features.
Axions were first introduced in connection with chiral symmetry but are now being looked for mainly as dark matter. In this paper we introduce a nonabelian analogue of axions which can also be potential candidates for dark matter. Their nonabelian symmetries, which are generalizations of the Peccei-Quinn symmetry, are interesting in their own right. Detailed analysis, using fermion measure and zeta function approaches shows that these symmetries are not anomalous.
We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an `invisible' axion arises from a single breaking of the gauge and global symmetries.
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete Zn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/Z2N and T6/Z2xZ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent Z2 symmetry is identified in a global Pati-Salam model, while global left-right symmetr…
In this paper, we construct a supersymmetric composite axion (c-axion) model based on the gauge group $SU(N)\times SU(M)$, which is one possible physical application of the N=1 duality. The dual of SU(M) is interpreted as the color gauge group. We illustrate the existence of c-axion for the case of one dual quark in the dual gauge group $SU(\tilde M)$.
Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review, these symmetries typically combine into a higher-group, a kind of non-abelian structure where symmetries that act on operators of different dimensions, such as points, lines, and strings, are mixed. We use this structure to derive model independent constraints on renormalization group flows that realize theories of axions at long distances. These give univer…
We study non-invertible global symmetries in $(3+1)$-dimensional axion electrodynamics with a massless axion and a massless photon. In addition to a previously known non-invertible 0-form shift symmetry of the axion, we find a non-invertible 1-form symmetry associated with the equation of motion for the photon. Correlation functions of non-invertible symmetry defects lead to invertible 1- and 2-form symmetry defects associated with Bianchi identities for the axion and photon. In terms of the correlation functions, we discuss several phenomena for extended objects, such as induced fractional el…
We consider a string inspired non-supersymmetric extension of the standard model with gauged anomalous U(1) flavor symmetries. Consistency requires the Green-Schwarz mechanism to cancel mixed anomalies. The additional required scalars provide Stuckelberg masses for the $Z'$ particles associated to the gauged flavor symmetry, so they decouple at low energies. Our models also include a complex scalar field $ϕ$ to generate Froggatt-Nielsen mass terms for light particles giving a partial solution to the fermion mass problem. A residual approximate (anomalous) global symmetry survives at low energi…
We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in $(3+1)$ dimensions. It is shown that the higher-form symmetries of this system are accompanied by a semistrict 3-group (2-crossed module) structure, which can be found by the correlation functions of symmetry generators of the higher-form symmetries. We argue that the Witten effect and anomalous Hall effect in the axion electrodynamics can be described in terms of 3-group transformations.
Berry phase in axion physics, SM global structure, and generalized symmetries
School of Physics, Peking University（北京大学物理学院）；School of Physics, Zhengzhou University（郑州大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Department of Physics, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院物理系）；Key Laboratory of Beam Technology of Ministry of Education, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院教育部光束技术重点实验室）；Institute of Radiation Technology, Beijing Academy of Science and Technology（北京市科学技术研究院辐射技术研究所）
We show that by imposing local $Z_{13}\otimes Z_3$ symmetries in an $SU(2)\otimes U(1)$ electroweak model we can implement an invisible axion in such a way that (i) the Peccei-Quinn symmetry is an automatic symmetry of the classical Lagrangian; and (ii) the axion is protected from semi classical gravitational effects. In order to be able to implement such a large discrete symmetry, and at the same time allow a general mixing in each charge sector, we introduce right-handed neutrinos and enlarge the scalar sector of the model. The domain wall problem is briefly considered.
We compute the form of the Lagrangian of N=1 supersymmetric theories with gauged axion symmetries. It turns out that there appear generalized Chern-Simons terms that were not considered in previous superspace formulations of general N=1 theories. Such gaugings appear in supergravities arising from flux compactifications of superstrings, as well as from Scherk-Schwarz generalized dimensional reduction in M-theory. We also present the dual superspace formulation where axion chiral multiplets are dualized into linear multiplets.
In this work, we discuss how the use of the symmetries well motivated in physics beyond the Standard model (BSM) can guarantee the high quality axions. We avoid to introduce symmetries only useful for addressing the axion quality problem. Rather, we rely on symmetries well motivated by other issues in BSM: supersymmetry, $U(1)_{\rm B-L}$ and the discrete R-symmetry $Z_{NR}$. We show that the interplay among these guarantees the high quality of the axion even for the gravitino mass and axion decay constant as large as $m_{3/2}=\mathcal{O}(10){\rm TeV}$ and $F_{a}=\mathcal{O}(10^{15}){\rm GeV}$ …
We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible 't Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.
Nonlinearly realized Abelian global symmetries can be reformulated as local shift symmetries gauged by three-form gauge fields. The anomalous symmetries of the Standard Model (such as Peccei-Quinn or $B+L$) can be dualized to local symmetries gauged by the Chern-Simons three-forms of the Standard Model gauge group. In this description the strong CP problem can be reformulated as the problem of a massless three-form field in QCD, which creates an arbitrary CP-violating constant four-form electric field in the vacuum. Both the axion as well as the massless quark solutions amount to simply Higgsi…
We find the full symmetries of the Wheeler-DeWitt equation for the Hawking and Page wormhole model and an axion-dilaton string cosmology. We show that the Wheeler-DeWitt Hamiltonian admits an U(1,1) hidden symmetry for the Hawking and Page model and U(2,1) for the axion-dilaton string cosmology. If we consider the existence of matter-energy renormalization, for each of these models we find that the Wheeler-DeWitt Hamiltonian accept an additional SL(2,R) dynamical symmetry. In this case, we show that the SL(2,R) dynamical symmetry generators transform the states from one energy Hilbert eigensub…
Continuous global symmetries are expected to be broken by gravity, which can lead to important phenomenological consequences. A prime example is the threat that this poses to the viability of the Peccei-Quinn solution to the strong CP problem. In this paper, we explore the impact of wormholes as a source of global symmetry breaking by gravity. We review the current status of wormholes and global symmetries and note that, surprisingly, the axion has a quality problem within non-perturbative Einstein gravity. Although these wormholes lead to a large breaking of global symmetries, we show that th…
We show that by introducing appropriate local $Z_N(N\geq13)$ symmetries in electroweak models it is possible to implement an automatic Peccei-Quinn symmetry keeping at the same time the axion protected against gravitational effects. Although we consider here only an extension of the standard model and a particular 3-3-1 model, the strategy can be used in any kind of electroweak model. An interesting feature of this 3-3-1 model is that if: {\it i)} we add right-handed neutrinos, {\it ii)} the conservation of the total lepton number, and {\it iii)} a $Z_2$ symmetry, the $Z_{13}$ and the chiral P…
The symmetry structure of axion-dilaton quantum string cosmology is investigated. The invariance of the string effective action under S-duality group, SU(1,1), facilitates solution of Wheeler-De Witt equation from group theoretic considerations; revealing existence of a new class of wave functions. We discover the an underlying ${W}$-infinity algebra in this formulation.
To obtain natural inflation with large tensor-to-scalar ratio in string framework, we need a special moduli stabilization mechanism which can separate the masses of real and imaginary components of Kähler moduli at different scales, and achieve a trans-Planckian axion decay constant from sub-Planckian axion decay constants. In this work, we stabilize the matter fields by F-terms and the real components of Kähler moduli by D-terms of two anomalous $U(1)_X\times U(1)_A$ symmetries strongly at high scales, while the corresponding axions remain light due to their independence on the Fayet-Iliopoul…
In this paper, we discuss the construction of Effective Field Theories (EFTs) in which a chiral fermion, charged under both gauge and global symmetries, is integrated out. Inspired by typical axion models, these symmetries can be spontaneously broken, and the global ones might also be anomalous. In this context, particular emphasis is laid on the derivative couplings of the Goldstone bosons to the fermions, as these lead to severe divergences and ambiguities when building the EFT. We show how to precisely solve these difficulties within the path integral formalism, by adapting the anomalous Wa…
The idea that the gravity-induced breaking of global symmetries is encoded in Planck-suppressed operators is not scale-invariant: heavy particles which have nothing to do with the UV completion of gravity can mediate the breaking and produce low-energy operators (partly) suppressed by their own mass scales. Such contributions from heavy fields are typically subdominant with respect to the least Planck-suppressed operators, unless the latter are forbidden, as is usual in solutions to the axion quality problem based on four-dimensional gauge symmetries. Therefore, with a focus on axion physics, …
The axion particle may or may not exist, but the axion field can be used, as shown here, in an explicitly local formulation of a chiral U(1) gauge theory with both classical and quantum gauge invariance. Nonabelian analogues of axion fields, which have recently been introduced, can be used, together with their special symmetries, in a similar construction of nonabelian chiral gauge theories. As in known cases, the gauge symmetry is broken and the gauge boson acquires a mass by swallowing the axions which are therefore not physical in this construction.
We investigate a higher-group structure of massless axion electrodynamics in $(3+1)$ dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily have a global semistrict 3-group (2-crossed module) structure, and exhibit 't Hooft anomalies of the 3-group. In particular, we find a cubic mixed 't Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.
We study higher-form symmetries and a higher group in the low energy limit of a $(3+1)$-dimensional axion electrodynamics with a massive axion and a massive photon. A topological field theory describing topological excitations with the axion-photon coupling, which we call a topological axion electrodynamics, is obtained in the low energy limit. Higher-form symmetries of the topological axion electrodynamics are specified by equations of motion and Bianchi identities. We find that there are induced anyons on the intersections of symmetry generators. By a link of worldlines of the anyons, we sho…
The group classification of models of axion electrodynamics with arbitrary self interaction of axionic field is carried out. It is shown that extensions of the basic Poincaré invariance of these models appear only for constant and exponential interactions. The related conservation laws are discussed. Using the Inönü-Wigner contraction the non-relativistic limit of equations of axion electrodynamics is found. An extended class of exact solutions for the electromagnetic and axion fields is obtained. Among them there are solutions including up to six arbitrary functions. In particular, solutions …
We discuss the energy scales of the explicit breaking terms of the global symmetries \USW~ needed for the quinessential axion (QA) and the ultra-light axion (ULA). The appropriate scale of QA is about $10^{8}$ GeV.
Global symmetries are expected to be violated by gravity, which may cause a serious problem to models based on these symmetries. A famous example is the Peccei-Quinn solution to the strong CP problem in QCD axion models; it requires a global U(1) symmetry to be respected with high quality, and even the Planck-scale suppressed operators that violate the U(1) symmetry would spoil this solution. Indeed, it is known that gravitational instantons do break the U(1) Peccei-Quinn symmetry and induce the U(1)-violating operators, bringing back the strong CP problem to the axion models. This conclusion …
A large class of new 4-D superstring vacua with non-trivial/singular geometries, spacetime supersymmetry and other background fields (axion, dilaton) are found. Killing symmetries are generic and are associated with non-trivial dilaton and antisymmetric tensor fields. Duality symmetries preserving N=2 superconformal invariance are employed to generate a large class of explicit metrics for non-compact 4-D Calabi-Yau manifolds with Killing symmetries.
We present a supersymmetric extension of the Standard Model (USSM-A) with an anomalous U(1) and Stueckelberg axions for anomaly cancellation, generalizing similar non-supersymmetric constructions. The model, built by a bottom-up approach, is expected to capture the low-energy supersymmetric description of axionic symmetries in theories with gauged anomalous abelian interactions, previously explored in the non-supersymmetric case for scenarios with intersecting branes. The choice of a USSM-like superpotential, with one extra singlet superfield and an extra abelian symmetry, allows a physical ax…
The axion-dilaton string effective action is expressed in Einstein frame metric in a manifestly S-duality invariant form. It is shown that the moduli can be redefined to describe surface of a 2+1 dimensional pseudosphere. The classical cosmological solutions are of axion-dilaton are revisited. The Wheeler De Witt equation for the system is exactly solved and complete set of eigenfunctions are presented. The wave function factorizes and the one depending on the moduli is obtained by appealing to the underlying S-duality symmetry. Axion and dilaton parametrize the coset SU(1,1)/U(1), the S-duali…
Nordita, KTH Royal Institute of Technology and Stockholm University（诺尔迪塔，皇家理工学院和斯德哥尔摩大学）；Center of Gravity, The Niels Bohr Institute, Copenhagen University（引力中心，尼尔斯·玻尔研究所，哥本哈根大学）
We analyze the quantum consistency of anomalous abelian models and of their effective field theories, rendered anomaly-free by a Wess-Zumino term, in the case of multiple abelian symmetries. These models involve the combined Higgs-Stuckelberg mechanism and predict a pseudoscalar axion-like field that mixes with the goldstones of the ordinary Higgs sector. We focus our study on the issue of unitarity of these models both before and after spontaneous symmetry breaking and detail the set of Ward identities and the organization of the loop expansion in the effective theory. The analysis is perform…
We find new solutions to real cubic constraints on $N=1$ chiral superfields transforming under global abelian symmetries. These solutions describe the low-energy dynamics of a goldstino interacting with an axion (both belonging to the same chiral superfield) with non-linearly realized supersymmetry. We show the relation between our model and the approach of Komargodski and Seiberg for describing goldstino-axion dynamics which uses orthogonal nilpotent superfields.
In four-dimensional axion electrodynamics, a Chern-Simons coupling of the form $θF \wedge F$ leads to a higher-group global symmetry between background gauge fields. At the same time, such a Chern-Simons coupling leads to a mixing between the Weak Gravity Conjectures for the axion and the gauge field, so that the charged excitations of a Weak Gravity Conjecture-satisfying axion string will also satisfy the Weak Gravity Conjecture for the gauge field. In this paper, we argue that these higher-group symmetries and this phenomenon of Weak Gravity Conjecture mixing are related to one another. We s…
Wrapped branes in string compactifications introduce a monodromy that extends the field range of individual closed-string axions to beyond the Planck scale. Furthermore, approximate shift symmetries of the system naturally control corrections to the axion potential. This suggests a general mechanism for chaotic inflation driven by monodromy-extended closed-string axions. We systematically analyze this possibility and show that the mechanism is compatible with moduli stabilization and can be realized in many types of compactifications, including warped Calabi-Yau manifolds and more general Ricc…
Motivated by recent discussions and the absence of exact global symmetries in UV completions of gravity we re-examine the axion quality problem (and naturalness issues more generally) using antisymmetric Kalb-Ramond (KR) fields rather than their pseudoscalar duals, as suggested by string and higher dimensional theories. Two types of axions can be identified: a model independent $S$-type axion dual to a two form $B_{μν}$ in 4D and a $T$-type axion coming directly as 4D scalar Kaluza-Klein (KK) components of higher-dimensional tensor fields. For $T$-type axions our conclusions largely agree with…
The recent detection of the cosmic microwave background polarimeter experiment BICEP2 of tensor fluctuations in the B-mode power spectrum basically excludes all plausible axion models where its decay constant is above $10^{13}$ GeV. Moreover, there are strong theoretical, astrophysical, and cosmological motivations for models involving, in addition to the axion, also axion-like particles (ALPs), with decay constants in the intermediate scale range, between $10^9$ GeV and $10^{13}$ GeV. Here, we present a general analysis of models with an axion and further ALPs and derive bounds on the relativ…
We study the general multi-axion systems, focusing on the possibility of large field inflation driven by axions. We find that through axion mixing from a non-diagonal metric on the moduli space and/or from Stückelberg coupling to a U(1) gauge field, an effectively super-Planckian decay constant can be generated without the need of "alignment" in the axion decay constants. We also investigate the consistency conditions related to the gauge symmetries in the multi-axion systems, such as vanishing gauge anomalies and the potential presence of generalized Chern-Simons terms. Our scenario applies g…
A generalization of Born-Infeld non-linear vacuum electrodynamics involving axion and dilaton fields is constructed with couplings dictated by electromagnetic duality and SL(2,R) symmetries in the weak field limit. Besides the Newtonian gravitational constant the model contains a single fundamental coupling parameter b0. In the absence of axion and dilaton interactions it reduces, in the limit as b0 tends to infinity, to Maxwell's linear vacuum theory while for finite b0 it reduces to the original Born-Infeld model. The spherically symmetric static sector of the theory is explored in a backgro…
In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T-duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to …
Recently the YbOH molecule has been suggested as a candidate to search for the electron electric dipole moment (eEDM) which violates spatial parity (P) and time-reversal (T) symmetries [I. Kozyryev and N. R. Hutzler, Phys. Rev. Lett. 119, 133002 (2017)]. In the present paper we show that the same system can be used to measure coupling constants of the interaction of electrons and nucleus with axionlike particles. The electron-nucleus interaction produced by the axion exchange induces T,P-violating a EDM of the whole molecular system. We express the corresponding T,P-violating energy shift prod…
Models of large-field inflation based on axion-like fields with shift symmetries can be simple and natural, and make a promising prediction of detectable primordial gravitational waves. The Weak Gravity Conjecture is known to constrain the simplest case in which a single compact axion descends from a gauge field in an extra dimension. We argue that the Weak Gravity Conjecture also constrains a variety of theories of multiple compact axions including N-flation and some alignment models. We show that other alignment models entail surprising consequences for how the mass spectrum of the theory va…
