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Monodromic transparency of axion domain walls

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Pith's one-line read This paper claims that QCD axion domain walls become nearly transparent to low-frequency photons at $E/N=8/3$, with reflection probability $\sim (\omega/m_a)^4$ and thermal pressure $\sim T^8$ instead of an exponential.

desk verdict Corrects the exponential suppression to a T^8 power law for E/N=8/3, with a genuine but scoped caveat about chiral-order stability. read the letter →

arxiv 2412.15085 v1 pith:YO7OQDS4 submitted 2024-12-19 hep-ph hep-th

Simone Blasi This is my paper · ORCID
classification hep-phhep-th
keywords QCDaxiondomainwallsaxion-photoncouplingmonodromicchiralperturbationtheorythermalfrictionbirefringenceE/Nanomalyratio
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the interaction of photons with QCD axion domain walls is governed by the full non-linear, monodromic axion-photon coupling $g(a)F\tilde{F}$, not by the standard linear coupling that is accurate only near a single vacuum. The central result is a cancellation: when the electromagnetic-to-color anomaly ratio takes the minimal-GUT value $E/N=8/3$, the net change of $g(a)$ across the wall vanishes, so long-wavelength photons reflect very little. The reflection probability scales as $R\simeq 2.16\,\alpha^2(\omega/m_a)^4$ for $\omega\ll m_a$, and the low-temperature friction from a thermal photon bath follows a power law, $\Delta P\propto v_w\alpha^2(T/m_a)^4T^4$, rather than the exponential $e^{-m_a/T}$ suppression of the original calculation. For generic anomaly ratios the low-temperature pressure is $\Delta P\propto (E/N-8/3)^2T^4$. The paper further shows that the wall's birefringence is controlled by the same monodromic charge and vanishes at $E/N=8/3$, and that reversing the quark mass hierarchy shifts the transparency to $E/N=2/3$.

What carries the argument

The central object is the monodromic axion-photon coupling $g(a)$ appearing in the effective interaction $(\alpha/4\pi)\,g(a)F_{\mu\nu}\tilde{F}^{\mu\nu}$, defined in Eq.~(2.20) after integrating out the pion. 'Monodromic' means $g(a+2\pi)-g(a)=2\pi n$ with integer monodromic charge $n=E-\tfrac{8}{3}N$; the coupling encodes axion-pion mixing for the $\mathcal{O}(1)$ field excursions that occur across strings and walls, where the linear coupling $g_{a\gamma\gamma}aF\tilde{F}$ is insufficient. This one function carries the argument: its derivative sources the photon equations of motion, its jump $\Delta[g(a)]_{\rm DW}=(E/N-\tfrac{8}{3})\pi$ fixes the reflection probability and the birefringence, and the vanishing of that jump at $E/N=8/3$ produces the $(\omega/m_a)^4$ transparency and the $T^8$ thermal pressure.

What would settle it

Compute the next-to-leading-order chiral correction to $g(a)$ — or repeat the analysis with three light flavors — and check whether the jump $\Delta[g(a)]$ across the wall at $E/N=8/3$ remains exactly zero. A nonzero jump would make $R$ tend to a constant $(\alpha^2/4)(\Delta g)^2$ as $\omega\to 0$ and change the low-temperature pressure from $T^8$ to $T^4$.

Watch

Extended reading notes

Core claim

Within two-flavor leading-order chiral perturbation theory the axion and neutral pion form a combined domain wall; once the pion is integrated out at tree level, the photon source is the derivative of $g(a)=\tan^{-1}\left[\sin(2Na)/(z^{-1}+\cos(2Na))\right]+(E-\tfrac{8}{3}N)a$. Across any wall between adjacent vacua the coupling jumps by $\Delta[g(a)]_{\rm DW}=(E/N-\tfrac{8}{3})\pi$. For minimal GUTs, $E/N=8/3$, so the jump is zero and the leading Born amplitude for photon reflection vanishes; the first non-zero contribution is $R_{8/3}\simeq 2.16\,\alpha^2(\omega/m_a)^4$. The pressure on a slowly moving wall in a low-temperature photon bath follows from this as $\Delta P^{8/3}\simeq v_w\,c\,\alpha^2\frac{2}{\pi^2}\Gamma(8)(T/m_a)^4T^4$ with $c\simeq 2.16$ and $\Gamma(8)=7!$, a power law rather than the exponential claimed in Ref.~[10]. Away from the special value, $R\simeq \frac{\alpha^2}{4}(E/N-\tfrac{8}{3})^2$ and $\Delta P\propto (E/N-\tfrac{8}{3})^2T^4$ at low temperature. The polarization rotation for light crossing the wall is $\Delta\Phi=\frac{\alpha}{2\pi}\Delta[g(a)]_{\rm DW}=\pm\frac{\alpha}{2}(E/N-\tfrac{8}{3})$, independent of frequency, and hence also vanishes at $E/N=8/3$.

Load-bearing premise

The exact transparency at $E/N=8/3$ rests on the tree-level two-flavor leading-order chiral perturbation theory description of the axion-pion wall; if higher-order chiral corrections, the strange quark, or the precise quark mass ratio $m_u/m_d$ alter the pion profile, the cancellation, the $(\omega/m_a)^4$ reflection law, and the $T^8$ pressure all receive corrections.

Editorial extensions

If this is right

  • At $E/N=8/3$, low-frequency photon scattering off axion domain walls is suppressed as $(\omega/m_a)^4$, so the walls are effectively transparent to the long-wavelength part of a thermal photon bath.
  • The resulting low-temperature friction on $E/N=8/3$ walls is $\Delta P\propto v_w\alpha^2(T/m_a)^4T^4$, not $e^{-m_a/T}$, which changes the predicted dynamics of the wall network and the gravitational-wave signal from its collapse.
  • For generic $E/N$, the low-temperature pressure is $\Delta P\propto (E/N-8/3)^2T^4$, while at high temperature it scales as $m_a^3T$ and is nearly independent of $E/N$.
  • Birefringence from crossing a wall is $\pm(\alpha/2)(E/N-8/3)$ for all frequencies, vanishing at $E/N=8/3$; a photon looping around an axion string accumulates $2N$ times this jump, so minimal-GUT string networks give no leading-order net rotation.
  • The cancellation is not tied to the exact quark masses: with $m_u>m_d$ it shifts to $E/N=2/3$, and in heavy QCD axion models with an aligned dark confining sector the $E/N=8/3$ transparency persists at low energies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If higher-order chiral corrections leave the cancellation intact, $E/N=8/3$ wall networks would experience much weaker late-time photon friction, which would alter the expected gravitational-wave spectrum and the relic abundance of domain walls; this is an inference beyond the paper's own conclusions.
  • The monodromic-charge logic suggests a general rule: any axion-like particle whose periodic photon coupling has vanishing jump across a defect will be transparent at low frequencies, so $E/N=8/3$ is one point in a family parameterized by the monodromic charge $n$.
  • A concrete testable extension is to recompute $g(a)$ with the strange quark included or at next-to-leading order in chiral perturbation theory; any non-zero $\Delta[g(a)]$ at $E/N=8/3$ would replace the $(\omega/m_a)^4$ law by a constant reflectivity and the $T^8$ pressure by $T^4$.
  • Future cosmic-birefringence observations of string-wall networks could in principle distinguish anomaly ratios: a null leading-order rotation would point to $E/N=8/3$ (or its mass-hierarchy-shifted analogue), while a rotation proportional to $\alpha$ would disfavor the special cancellation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The manuscript revisits photon scattering off QCD axion domain walls using the non-linear monodromic axion-photon coupling g(a)F\tilde F introduced in Ref. [41]. After integrating out the pion at tree level in two-flavor leading-order chiral perturbation theory, the author derives g(a) in Eq. (2.20) and shows that its change across a wall is (E/N - 8/3)π (Eqs. (2.16) and (2.22)). For the minimal GUT value E/N = 8/3 this vanishes, leading to a strongly suppressed low-frequency reflection probability R ~ c α² (ω/m_a)^4 (Eq. (2.29)) and a thermal pressure ΔP ∝ T^8 (Eq. (2.34)) instead of the exponential suppression claimed in Ref. [10]. The author also computes the birefringence of the walls, finding a general result ΔΦ = (α/2π)Δ[g] that vanishes at E/N = 8/3, and studies two variations: mu > md, where the cancellation shifts to E/N = 2/3, and a heavy QCD axion, where the cancellation at E/N = 8/3 persists in the low-frequency limit. The analytic results are compared with numerical solutions of the scattering problem in Figs. 2 and 3.

Significance. If correct, the paper provides a parameter-free derivation of a surprising power-law friction law for axion domain walls, resolving a discrepancy between Ref. [10] and its preprint version [39] and highlighting the importance of non-linear axion couplings for defect electrodynamics. The analytic expressions are checked against numerical solutions of the scattering equation, and the paper makes a falsifiable prediction for the low-temperature pressure (T^8 rather than exponential). The extension to heavy axions and to the inverted mass hierarchy usefully identifies which features are model-dependent. The central derivation is transparent and does not rely on fitted parameters; the numerical implementation is reproducible from the stated formulas.

major comments (1)
  1. [Sec. 2.1, Eqs. (2.16), (2.22), (2.27), (2.29), and Sec. 3.1] The exact cancellation Δ[g] = 0 at E/N = 8/3 rests on the two-flavor leading-order chiral potential (2.13), whose second vacuum lies exactly at (a, π0) = (π, -π) in the Qa = I/2 basis. This endpoint is not protected by the anomaly structure: Sec. 3.1 shows that for mu > md the same LO potential moves the cancellation to E/N = 2/3, and no argument is given that O(p^4) chiral corrections or the strange quark leave the endpoint unchanged. A shift δ in the pion VEV at the second vacuum would give a constant contribution R(ω→0) ≈ α²δ²/4π² in Eq. (2.27) and add a T^4 term to the pressure in Eq. (2.34) that dominates for T ≲ |δ| m_a. Moreover, the ω^4 scaling in Eq. (2.29) requires not only Δ[g] = 0 but also the vanishing of the area ∫g(z)dz, which follows from the symmetry of the LO potential; a generic NLO perturbation would typically give R ∝ ω² instead. The paper should either estimate these corrections and show they are negligible for physical QCD, or state explicitly that the transparency and the T^8 law are predictions of the two-flavor LO EFT only.
minor comments (4)
  1. [Sec. 2.1, Eq. (2.29)] The numerical coefficient c ≈ 2.16 is computed with a cosine domain-wall profile rather than the actual potential (2.21). Since this coefficient enters the pressure prediction (2.34), please provide the value of c obtained with the full potential, or estimate the error introduced by the cosine approximation.
  2. [Sec. 3.2, Eqs. (3.7) and (3.11)] The coefficient c_H = 6.08 relies on the pion profile (3.7) taken from Ref. [24]. If the exact solution of Eq. (3.6) differs, the numerical value of c_H may change; a short comment on the accuracy of this approximation would be helpful.
  3. [Title and Sec. 2.1] The term "transparency" could be misread as exact invisibility; in fact the reflection is suppressed as (ω/m_a)^4 at low frequencies. Consider adding a clarifying phrase such as "asymptotic transparency" in the introduction.
  4. [Sec. 2.1, discussion after Eq. (2.27)] The statement that the reflection probability cannot distinguish photon helicity at leading order is correct for |R±|², but the helicity-dependent phases in Eq. (2.25) may merit a brief clarification to avoid confusion.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the E/N=8/3 transparency follows from the LO two-flavor χPT pion endpoint, and the R∝ω^4 and ΔP∝T^8 laws are derived Born/integral consequences, not fitted inputs.

full rationale

The central derivation is self-contained against its stated assumptions. It starts from the two-flavor LO χPT potential (2.13), its degenerate vacua (2.15), and the pion potential minimum condition (2.17). The endpoint difference β_R − β_L = (E/N − 8/3)π in Eq. (2.16) is computed directly from those vacua, so the E/N=8/3 endpoint condition is a property of the stated EFT, not an adjustable parameter. Eq. (2.20) obtains g(a) by tree-level integrating out the pion, and Eq. (2.22) repeats the same endpoint difference; the cancellation is therefore a derived algebraic result. The reflection formula (2.27) is the standard Born integral, and the ω^4 scaling at E/N=8/3 follows from the vanishing of Δg and of the first moment of the odd wall profile; the O(1) coefficient c is evaluated using a declared cosine ansatz that affects only that numerical constant. The thermal pressure (2.34) is then the integral of R(ω) against the photon distribution (2.32); no quantity is fitted to make the T^8 term appear. Self-citations are auxiliary rather than load-bearing: Ref. [41] is used for context and the paper explicitly says it uses 'a different but equivalent form' of g(a); Ref. [22] co-cites the standard Arnold formula [60]; Ref. [24] supplies only the approximate pion profile used for the heavy-axion numerical coefficient c_H. The fragility of the cancellation under mu > md is explicitly derived in Sec. 3.1, which is a sensitivity statement, not a circularity. The derivation chain from χPT potential to transparency, reflection, and pressure is therefore open and checkable, with no step that reduces to its own output by construction.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No parameters are fitted to data. E/N, z, m_a, and m_pi are inputs from the model and QCD, and the coefficients c and c_H are computed numerically from stated profiles. The main assumptions are about the low-energy effective theory, the wall profiles, and the regime of validity, all stated in the text.

assumptions (6)
  • domain assumption Two-flavor leading-order chiral perturbation theory with the Wess-Zumino-Witten term describes the axion-pion-photon system below the QCD confinement scale.
    Invoked in Sec. 2 to derive Eq. (2.9) and the coupling g(a) in Eq. (2.20); neglects strange quark and higher-order corrections.
  • domain assumption The pion can be integrated out at tree level by solving the stationarity equation, valid for m_pi^2 much greater than m_a^2, i.e. F_a much greater than f_pi.
    Used in Sec. 2.1, Eq. (2.17), to reduce the two-field problem to the single-field coupling g(a).
  • standard math Born approximation at leading order in the fine-structure constant alpha is sufficient for the reflection and transmission amplitudes.
    Used in Eq. (2.26) and the pressure integrals; the smallness of alpha and the numerical checks in Fig. 2 support this.
  • domain assumption The wall is planar, thin compared with the thermal scales, and photon scattering can be treated in isolation.
    Assumed in Sec. 2.2 and valid for T much less than m_a; the paper cites Ref. [38] for collective plasma effects at higher temperatures.
  • domain assumption Approximate kink profiles, such as a(z) = (2/N) arctan(e^{m_a z}) and pi0(z) = -2 arctan(e^{m_pi z}), capture the domain wall solutions.
    Used to compute the coefficients c approximately 2.16 and c_H approximately 6.08 in Eqs. (2.29) and (3.11); exact profiles would change only O(1) coefficients.
  • domain assumption For the heavy QCD axion, an additional confining sector is uncharged under the Standard Model and aligned with QCD.
    Assumed in Sec. 3.2, Eq. (3.4), so that the minima of the full potential are unchanged.

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Cite this review

Pith. "Pith review of Monodromic transparency of axion domain walls." pith.science (2026). https://pith.science/paper/YO7OQDS4

@misc{pith2026241215085,
  author       = {Pith},
  title        = {Pith review of: Monodromic transparency of axion domain walls},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YO7OQDS4}},
  note         = {Machine review of arXiv:2412.15085}
}
abstract

We revisit the study of light interacting with QCD axion domain walls from the perspective of the non-linear axion coupling to photons, $g(a) F \tilde F$, which encodes the effects related to the breaking of the axion shift symmetry including the well-known mixing with meson states. As the axion makes an $\mathcal{O}(1)$ excursion of its fundamental period around strings and domain walls, the standard linear coupling to photons is generally insufficient to accurately describe the interaction of light with the defects, and one needs to consider the full structure of $g(a)$. We take this into account in evaluating the friction experienced by axion domain walls moving in a thermal bath of photons, as well as in deriving the birefringent properties of the walls. This clarifies some results in the literature dealing with a special cancellation that takes place for the QCD axion with the electromagnetic and color anomaly as predicted by minimal Grand Unified Theories.

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Reference graph

Works this paper leans on

67 extracted references · 15 canonical work pages · cited by 1 Pith paper

  1. [10]

    Huang and P

    M.C. Huang and P. Sikivie, The Structure of Axionic Domain Walls , Phys. Rev. D 32 (1985) 1560

    work page 1985

  2. [41]

    Agrawal and A

    P. Agrawal and A. Platschorre, The monodromic axion-photon coupling , JHEP 01 (2024) 169 [2309.03934]

    arXiv 2024

  3. [39]

    Huang and P

    M.C. Huang and P. Sikivie, The Structure of Axionic Domain Walls , KEK Preprint (1985)

    work page 1985

  4. [1]

    Peccei and H.R

    R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons , Phys. Rev. Lett. 38 (1977) 1440

    1977

  5. [2]

    Weinberg, A New Light Boson? , Phys

    S. Weinberg, A New Light Boson? , Phys. Rev. Lett. 40 (1978) 223

    1978

  6. [3]

    Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons , Phys

    F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons , Phys. Rev. Lett. 40 (1978) 279

    1978

  7. [4]

    Kim, Weak Interaction Singlet and Strong CP Invariance , Phys

    J.E. Kim, Weak Interaction Singlet and Strong CP Invariance , Phys. Rev. Lett. 43 (1979) 103

    1979

  8. [5]

    Shifman, A.I

    M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can Confinement Ensure Natural CP Invariance of Strong Interactions? , Nucl. Phys. B 166 (1980) 493

    1980

Show all 67 references
  1. [6]

    Zhitnitsky, On Possible Suppression of the Axion Hadron Interactions

    A.R. Zhitnitsky, On Possible Suppression of the Axion Hadron Interactions. (In Russian) , Sov. J. Nucl. Phys. 31 (1980) 260

    1980

  2. [7]

    M. Dine, W. Fischler and M. Srednicki, A Simple Solution to the Strong CP Problem with a Harmless Axion , Phys. Lett. B 104 (1981) 199

    1981

  3. [8]

    Vilenkin and A.E

    A. Vilenkin and A.E. Everett, Cosmic Strings and Domain Walls in Models with Goldstone and PseudoGoldstone Bosons , Phys. Rev. Lett. 48 (1982) 1867

    1982

  4. [9]

    Sikivie, Of Axions, Domain Walls and the Early Universe , Phys

    P. Sikivie, Of Axions, Domain Walls and the Early Universe , Phys. Rev. Lett. 48 (1982) 1156

    1982

  5. [11]

    Bardeen and S.H.H

    W.A. Bardeen and S.H.H. Tye, Current Algebra Applied to Properties of the Light Higgs Boson, Phys. Lett. B 74 (1978) 229

    1978

  6. [12]

    Sikivie, On the Interaction of Magnetic Monopoles With Axionic Domain Walls , Phys

    P. Sikivie, On the Interaction of Magnetic Monopoles With Axionic Domain Walls , Phys. Lett. B 137 (1984) 353

    1984

  7. [13]

    Ganoulis and M

    N. Ganoulis and M. Hatzis, Light Scattering by an Axionic Domain Wall , Mod. Phys. Lett. A 1 (1986) 409

    1986

  8. [14]

    Wilczek, Two Applications of Axion Electrodynamics , Phys

    F. Wilczek, Two Applications of Axion Electrodynamics , Phys. Rev. Lett. 58 (1987) 1799

    1987

  9. [15]

    Carroll, G.B

    S.M. Carroll, G.B. Field and R. Jackiw, Limits on a lorentz- and parity-violating modification of electrodynamics, Phys. Rev. D 41 (1990) 1231. – 16 –

    1990

  10. [16]

    Harari and P

    D. Harari and P. Sikivie, Effects of a Nambu-Goldstone boson on the polarization of radio galaxies and the cosmic microwave background , Phys. Lett. B 289 (1992) 67

    1992

  11. [17]

    Hiramatsu, M

    T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion cosmology with long-lived domain walls , JCAP 01 (2013) 001 [ 1207.3166]

    2013 arXiv

  12. [18]

    Higaki, K.S

    T. Higaki, K.S. Jeong, N. Kitajima, T. Sekiguchi and F. Takahashi, Topological Defects and nano-Hz Gravitational Waves in Aligned Axion Models , JHEP 08 (2016) 044 [ 1606.05552]

    2016 arXiv

  13. [19]

    Chiang and B.-Q

    C.-W. Chiang and B.-Q. Lu, Testing clockwork axion with gravitational waves , JCAP 05 (2021) 049 [ 2012.14071]

    2021 arXiv

  14. [20]

    Zambujal Ferreira, A

    R. Zambujal Ferreira, A. Notari, O. Pujol` as and F. Rompineve, High Quality QCD Axion at Gravitational Wave Observatories , Phys. Rev. Lett. 128 (2022) 141101 [ 2107.07542]

    2022 arXiv

  15. [21]

    Gelmini, A

    G.B. Gelmini, A. Simpson and E. Vitagliano, Gravitational waves from axionlike particle cosmic string-wall networks , Phys. Rev. D 104 (2021) 061301 [ 2103.07625]

    2021 arXiv

  16. [22]

    Blasi, A

    S. Blasi, A. Mariotti, A. Rase, A. Sevrin and K. Turbang, Friction on ALP domain walls and gravitational waves, JCAP 04 (2023) 008 [ 2210.14246]

    2023 arXiv

  17. [23]

    Bai, T.-K

    Y. Bai, T.-K. Chen and M. Korwar, QCD-collapsed domain walls: QCD phase transition and gravitational wave spectroscopy, JHEP 12 (2023) 194 [ 2306.17160]

    2023 arXiv

  18. [24]

    Blasi, A

    S. Blasi, A. Mariotti, A. Rase and A. Sevrin, Axionic domain walls at Pulsar Timing Arrays: QCD bias and particle friction , JHEP 11 (2023) 169 [ 2306.17830]

    2023 arXiv

  19. [25]

    Kitajima, J

    N. Kitajima, J. Lee, K. Murai, F. Takahashi and W. Yin, Gravitational waves from domain wall collapse, and application to nanohertz signals with QCD-coupled axions , Phys. Lett. B 851 (2024) 138586 [ 2306.17146]

    2024 arXiv

  20. [26]

    Lu, C.-W

    B.-Q. Lu, C.-W. Chiang and T. Li, Clockwork axion footprint on nanohertz stochastic gravitational wave background, Phys. Rev. D 109 (2024) L101304 [ 2307.00746]

    2024 arXiv

  21. [27]

    Ferreira, A

    R.Z. Ferreira, A. Notari, O. Pujol` as and F. Rompineve, Collapsing domain wall networks: impact on pulsar timing arrays and primordial black holes , JCAP 06 (2024) 020 [2401.14331]

    2024 arXiv

  22. [28]

    J. Lee, K. Murai, F. Takahashi and W. Yin, More is Different: Multi-Axion Dynamics Changes Topological Defect Evolution, 2409.09749

    arXiv

  23. [29]

    Gelmini, A

    G.B. Gelmini, A. Simpson and E. Vitagliano, Catastrogenesis: DM, GWs, and PBHs from ALP string-wall networks , JCAP 02 (2023) 031 [ 2207.07126]

    2023 arXiv

  24. [30]

    O’Hare, G

    C.A.J. O’Hare, G. Pierobon, J. Redondo and Y.Y.Y. Wong, Simulations of axionlike particles in the postinflationary scenario , Phys. Rev. D 105 (2022) 055025 [ 2112.05117]

    2022 arXiv

  25. [31]

    Gorghetto and E

    M. Gorghetto and E. Hardy, Post-inflationary axions: a minimal target for axion haloscopes , JHEP 05 (2023) 030 [ 2212.13263]

    2023 arXiv

  26. [32]

    Beyer and S

    K.A. Beyer and S. Sarkar, Ruling out light axions: The writing is on the wall , SciPost Phys. 15 (2023) 003 [ 2211.14635]

    2023 arXiv

  27. [33]

    Daido, N

    R. Daido, N. Kitajima and F. Takahashi, Axion domain wall baryogenesis , JCAP 07 (2015) 046 [1504.07917]

    2015 arXiv

  28. [34]

    Mariotti, X

    A. Mariotti, X. Nagels, A. Rase and M. Vanvlasselaer, DW-genesis: baryon number from domain wall network collapse , 2411.13494. – 17 –

    arXiv

  29. [35]

    Ferrer, E

    F. Ferrer, E. Masso, G. Panico, O. Pujolas and F. Rompineve, Primordial Black Holes from the QCD axion , Phys. Rev. Lett. 122 (2019) 101301 [ 1807.01707]

    2019 arXiv

  30. [36]

    Gelmini, J

    G.B. Gelmini, J. Hyman, A. Simpson and E. Vitagliano, Primordial black hole dark matter from catastrogenesis with unstable pseudo-Goldstone bosons , JCAP 06 (2023) 055 [2303.14107]

    2023 arXiv

  31. [37]

    Dunsky and M

    D.I. Dunsky and M. Kongsore, Primordial black holes from axion domain wall collapse , JHEP 06 (2024) 198 [ 2402.03426]

    2024 arXiv

  32. [38]

    Hassan, G.R

    S. Hassan, G.R. Kane, J. March-Russell and G. Obied, Chern-Simons Induced Thermal Friction on Axion Domain Walls , 2410.19906

    arXiv

  33. [40]

    Agrawal, M

    P. Agrawal, M. Nee and M. Reig, Axion couplings in grand unified theories , JHEP 10 (2022) 141 [2206.07053]

    2022 arXiv

  34. [42]

    Agrawal, J

    P. Agrawal, J. Fan, M. Reece and L.-T. Wang, Experimental Targets for Photon Couplings of the QCD Axion , JHEP 02 (2018) 006 [ 1709.06085]

    2018 arXiv

  35. [43]

    Fraser and M

    K. Fraser and M. Reece, Axion Periodicity and Coupling Quantization in the Presence of Mixing, JHEP 05 (2020) 066 [ 1910.11349]

    2020 arXiv

  36. [44]

    Agrawal, A

    P. Agrawal, A. Hook and J. Huang, A CMB Millikan experiment with cosmic axiverse strings, JHEP 07 (2020) 138 [ 1912.02823]

    2020 arXiv

  37. [45]

    Takahashi and W

    F. Takahashi and W. Yin, Kilobyte Cosmic Birefringence from ALP Domain Walls , JCAP 04 (2021) 007 [ 2012.11576]

    2021 arXiv

  38. [46]

    Jain, A.J

    M. Jain, A.J. Long and M.A. Amin, Cmb birefringence from ultralight-axion string networks , Journal of Cosmology and Astroparticle Physics 2021 (2021) 055

    2021

  39. [47]

    Kitajima, F

    N. Kitajima, F. Kozai, F. Takahashi and W. Yin, Power spectrum of domain-wall network, and its implications for isotropic and anisotropic cosmic birefringence , Journal of Cosmology and Astroparticle Physics 2022 (2022) 043

    2022

  40. [48]

    Gonzalez, N

    D. Gonzalez, N. Kitajima, F. Takahashi and W. Yin, Stability of domain wall network with initial inflationary fluctuations and its implications for cosmic birefringence , Phys. Lett. B 843 (2023) 137990 [ 2211.06849]

    2023 arXiv

  41. [49]

    M. Jain, R. Hagimoto, A.J. Long and M.A. Amin, Searching for axion-like particles through cmb birefringence from string-wall networks , Journal of Cosmology and Astroparticle Physics 2022 (2022) 090

    2022

  42. [50]

    Ferreira, S

    R.Z. Ferreira, S. Gasparotto, T. Hiramatsu, I. Obata and O. Pujolas, Axionic defects in the CMB: birefringence and gravitational waves , JCAP 05 (2024) 066 [ 2312.14104]

    2024 arXiv

  43. [51]

    Hagimoto, A.J

    R. Hagimoto, A.J. Long and M.A. Amin, Extracting Axion String Network Parameters from Simulated CMB Birefringence Maps using Convolutional Neural Networks , 2411.05002

    arXiv

  44. [52]

    J. Lee, K. Murai, F. Takahashi and W. Yin, Induced domain walls of QCD axion, and gravitational waves, JCAP 10 (2024) 038 [ 2407.09478]

    2024 arXiv

  45. [53]

    Gan, L.-T

    X. Gan, L.-T. Wang and H. Xiao, Detecting axion dark matter with black hole polarimetry , Phys. Rev. D 110 (2024) 063039 [ 2311.02149]. – 18 –

    2024 arXiv

  46. [54]

    Grilli di Cortona, E

    G. Grilli di Cortona, E. Hardy, J. Pardo Vega and G. Villadoro, The QCD axion, precisely , JHEP 01 (2016) 034 [ 1511.02867]

    2016 arXiv

  47. [55]

    Wess and B

    J. Wess and B. Zumino, Consequences of anomalous Ward identities , Phys. Lett. B 37 (1971) 95

    1971

  48. [56]

    Witten, Global Aspects of Current Algebra , Nucl

    E. Witten, Global Aspects of Current Algebra , Nucl. Phys. B 223 (1983) 422

    1983

  49. [57]

    Lu, M.-L

    Z.-Y. Lu, M.-L. Du, F.-K. Guo, U.-G. Meißner and T. Vonk, QCD θ-vacuum energy and axion properties, JHEP 05 (2020) 001 [ 2003.01625]

    2020 arXiv

  50. [58]

    Forbes and A.R

    M.M. Forbes and A.R. Zhitnitsky, Domain walls in QCD , JHEP 10 (2001) 013 [hep-ph/0008315]

    2001 arXiv

  51. [59]

    Favitta, I.H

    A.M. Favitta, I.H. Brevik and M.M. Chaichian, Axion electrodynamics: Green ’s functions, zero-point energy and optical activity , Annals Phys. 455 (2023) 169396 [ 2302.13129]

    2023 arXiv

  52. [60]

    Arnold, One loop fluctuation - dissipation formula for bubble wall velocity , Phys

    P.B. Arnold, One loop fluctuation - dissipation formula for bubble wall velocity , Phys. Rev. D 48 (1993) 1539 [ hep-ph/9302258]

    1993 arXiv

  53. [61]

    Tye, A Superstrong Force With a Heavy Axion , Phys

    S.H.H. Tye, A Superstrong Force With a Heavy Axion , Phys. Rev. Lett. 47 (1981) 1035

    1981

  54. [62]

    Berezhiani, L

    Z. Berezhiani, L. Gianfagna and M. Giannotti, Strong CP problem and mirror world: The Weinberg-Wilczek axion revisited, Phys. Lett. B 500 (2001) 286 [ hep-ph/0009290]

    2001 arXiv

  55. [63]

    Dimopoulos, A

    S. Dimopoulos, A. Hook, J. Huang and G. Marques-Tavares, A collider observable QCD axion, JHEP 11 (2016) 052 [ 1606.03097]

    2016 arXiv

  56. [64]

    Gherghetta, N

    T. Gherghetta, N. Nagata and M. Shifman, A Visible QCD Axion from an Enlarged Color Group, Phys. Rev. D 93 (2016) 115010 [ 1604.01127]

    2016 arXiv

  57. [65]

    Agrawal and K

    P. Agrawal and K. Howe, Factoring the Strong CP Problem , JHEP 12 (2018) 029 [1710.04213]

    2018 arXiv

  58. [66]

    A. Hook, S. Kumar, Z. Liu and R. Sundrum, High Quality QCD Axion and the LHC , Phys. Rev. Lett. 124 (2020) 221801 [ 1911.12364]

    2020 arXiv

  59. [67]

    Gherghetta and M.D

    T. Gherghetta and M.D. Nguyen, A Composite Higgs with a Heavy Composite Axion , JHEP 12 (2020) 094 [ 2007.10875]. – 19 –

    2020 arXiv

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Reviewed August 11, 2026 · model on record in the stance chip above.