Abstract
We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral symmetry is due to the background axion field. We compute the contributions to this anomalous Ward identity due to the pseudoscalar field alone, which arise in Minkowski space, as well as the effects due to an interaction with an external gravitational field. For the case of massless fermions, these interactions induce terms in the axion effective action that can be removed by the addition of local counterterms. We demonstrate that these counterterms are generated by the transformation of the path integral measure when transforming the theory from a form where the chiral symmetry is manifest to one where the symmetry is only apparent after using the classical equations of motion. We work perturbatively in Minkowski space and include the effects of interactions with a linearized gravitational field. Using the heat kernel method, we study the transformation properties of the path integral measure, and include the effects of non-linear gravity as well as interactions with gauge fields. Finally, we verify our relation by considering derivatively coupled fermions during pseudoscalar-driven inflation and computing the divergence of the axial current in de Sitter spacetime.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
J. S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
S. L. Adler and W. A. Bardeen, Absence of higher order corrections in the anomalous axial vector divergence equation, Phys. Rev. 182 (1969) 1517 [INSPIRE].
W. A. Bardeen, Anomalous Ward identities in spinor field theories, Phys. Rev. 184 (1969) 1848 [INSPIRE].
K. Fujikawa, Path Integral Measure for Gauge Invariant Fermion Theories, Phys. Rev. Lett. 42 (1979) 1195 [INSPIRE].
K. Fujikawa, Path Integral for Gauge Theories with Fermions, Phys. Rev. D 21 (1980) 2848 [Erratum ibid. 22 (1980) 1499] [INSPIRE].
H. B. Nielsen and M. Ninomiya, Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. B 130 (1983) 389 [INSPIRE].
V. Domcke, Y. Ema, K. Mukaida and R. Sato, Chiral Anomaly and Schwinger Effect in Non-Abelian Gauge Theories, JHEP 03 (2019) 111 [arXiv:1812.08021] [INSPIRE].
T. Kimura, Divergence of axial-vector current in the gravitational field, Prog. Theor. Phys. 42 (1969) 1191 [INSPIRE].
R. Delbourgo and A. Salam, The gravitational correction to pcac, Phys. Lett. B 40 (1972) 381 [INSPIRE].
R. Delbourgo and A. Salam, PCAC anomalies and gravitation, IC-72-86 (1972).
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
S. H.-S. Alexander, M. E. Peskin and M. M. Sheikh-Jabbari, Leptogenesis from gravity waves in models of inflation, Phys. Rev. Lett. 96 (2006) 081301 [hep-th/0403069] [INSPIRE].
P. Adshead, A. J. Long and E. I. Sfakianakis, Gravitational Leptogenesis, Reheating, and Models of Neutrino Mass, Phys. Rev. D 97 (2018) 043511 [arXiv:1711.04800] [INSPIRE].
F. R. Klinkhamer and N. S. Manton, A Saddle Point Solution in the Weinberg-Salam Theory, Phys. Rev. D 30 (1984) 2212 [INSPIRE].
J. A. Harvey and M. S. Turner, Cosmological baryon and lepton number in the presence of electroweak fermion number violation, Phys. Rev. D 42 (1990) 3344 [INSPIRE].
P. Adshead and E. I. Sfakianakis, Fermion production during and after axion inflation, JCAP 11 (2015) 021 [arXiv:1508.00891] [INSPIRE].
P. Adshead and E. I. Sfakianakis, Leptogenesis from left-handed neutrino production during axion inflation, Phys. Rev. Lett. 116 (2016) 091301 [arXiv:1508.00881] [INSPIRE].
P. Adshead, L. Pearce, M. Peloso, M. A. Roberts and L. Sorbo, Phenomenology of fermion production during axion inflation, JCAP 06 (2018) 020 [arXiv:1803.04501] [INSPIRE].
P. Adshead, L. Pearce, M. Peloso, M. A. Roberts and L. Sorbo, Gravitational waves from fermion production during axion inflation, JCAP 10 (2019) 018 [arXiv:1904.10483] [INSPIRE].
L.-T. Wang and Z.-Z. Xianyu, In Search of Large Signals at the Cosmological Collider, JHEP 02 (2020) 044 [arXiv:1910.12876] [INSPIRE].
M. A. Roberts and L. Sorbo, Reviving chaotic inflation with fermion production: a supergravity model, JCAP 06 (2021) 047 [arXiv:2101.01796] [INSPIRE].
V. Domcke and K. Mukaida, Gauge Field and Fermion Production during Axion Inflation, JCAP 11 (2018) 020 [arXiv:1806.08769] [INSPIRE].
V. Domcke, B. von Harling, E. Morgante and K. Mukaida, Baryogenesis from axion inflation, JCAP 10 (2019) 032 [arXiv:1905.13318] [INSPIRE].
V. Domcke, Y. Ema and K. Mukaida, Chiral Anomaly, Schwinger Effect, Euler-Heisenberg Lagrangian, and application to axion inflation, JHEP 02 (2020) 055 [arXiv:1910.01205] [INSPIRE].
V. Domcke, Y. Ema, K. Mukaida and M. Yamada, Spontaneous Baryogenesis from Axions with Generic Couplings, JHEP 08 (2020) 096 [arXiv:2006.03148] [INSPIRE].
V. Domcke, Y. Ema and K. Mukaida, Axion assisted Schwinger effect, JHEP 05 (2021) 001 [arXiv:2101.05192] [INSPIRE].
V. Domcke, K. Schmitz and T. You, Cosmological Relaxation through the Dark Axion Portal, arXiv:2108.11295 [INSPIRE].
L. Mirzagholi, A. Maleknejad and K. D. Lozanov, Production and backreaction of fermions from axion-SU(2) gauge fields during inflation, Phys. Rev. D 101 (2020) 083528 [arXiv:1905.09258] [INSPIRE].
A. Maleknejad, Dark Fermions and Spontaneous C P violation in SU(2)-axion Inflation, JHEP 07 (2020) 154 [arXiv:1909.11545] [INSPIRE].
A. Maleknejad, SU(2)R and its axion in cosmology: A common origin for inflation, cold sterile neutrinos, and baryogenesis, Phys. Rev. D 104 (2021) 083518 [arXiv:2012.11516] [INSPIRE].
A. Maleknejad, Chiral anomaly in SU(2)R -axion inflation and the new prediction for particle cosmology, JHEP 06 (2021) 113 [arXiv:2103.14611] [INSPIRE].
P. Agrawal, J. Fan and M. Reece, Clockwork Axions in Cosmology: Is Chromonatural Inflation Chrononatural?, JHEP 10 (2018) 193 [arXiv:1806.09621] [INSPIRE].
J. Quevillon and C. Smith, Axions are blind to anomalies, Eur. Phys. J. C 79 (2019) 822 [arXiv:1903.12559] [INSPIRE].
M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading, MA, U.S.A. (1995).
A. Landete, J. Navarro-Salas and F. Torrenti, Adiabatic regularization for spin-1/2 fields, Phys. Rev. D 88 (2013) 061501 [arXiv:1305.7374] [INSPIRE].
A. Landete, J. Navarro-Salas and F. Torrenti, Adiabatic regularization and particle creation for spin one-half fields, Phys. Rev. D 89 (2014) 044030 [arXiv:1311.4958] [INSPIRE].
A. del Rio, J. Navarro-Salas and F. Torrenti, Renormalized stress-energy tensor for spin-1/2 fields in expanding universes, Phys. Rev. D 90 (2014) 084017 [arXiv:1407.5058] [INSPIRE].
L. E. Parker and D. Toms, Quantum Field Theory in Curved Spacetime: Quantized Field and Gravity, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (2009) [DOI] [INSPIRE].
D. V. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].
N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (1984) [DOI] [INSPIRE].
J. Quevillon, C. Smith and P. N. H. Vuong, Axion Effective Action, arXiv:2112.00553 [INSPIRE].
S. V. Sushkov, Exact cosmological solutions with nonminimal derivative coupling, Phys. Rev. D 80 (2009) 103505 [arXiv:0910.0980] [INSPIRE].
E. N. Saridakis and S. V. Sushkov, Quintessence and phantom cosmology with non-minimal derivative coupling, Phys. Rev. D 81 (2010) 083510 [arXiv:1002.3478] [INSPIRE].
C. Gao, When scalar field is kinetically coupled to the Einstein tensor, JCAP 06 (2010) 023 [arXiv:1002.4035] [INSPIRE].
C. Germani and A. Kehagias, New Model of Inflation with Non-minimal Derivative Coupling of Standard Model Higgs Boson to Gravity, Phys. Rev. Lett. 105 (2010) 011302 [arXiv:1003.2635] [INSPIRE].
C. Germani and A. Kehagias, Cosmological Perturbations in the New Higgs Inflation, JCAP 05 (2010) 019 [Erratum ibid. 06 (2010) E01] [arXiv:1003.4285] [INSPIRE].
C. Germani and Y. Watanabe, UV-protected (Natural) Inflation: Primordial Fluctuations and non-Gaussian Features, JCAP 07 (2011) 031 [Addendum ibid. 07 (2011) A01] [arXiv:1106.0502] [INSPIRE].
C. Germani, Slow Roll Inflation: A Somehow Different Perspective, Rom. J. Phys. 57 (2012) 841 [arXiv:1112.1083] [INSPIRE].
S. Folkerts, C. Germani and J. Redondo, Axion Dark Matter and Planck favor non-minimal couplings to gravity, Phys. Lett. B 728 (2014) 532 [arXiv:1304.7270] [INSPIRE].
Y. Watanabe and E. Komatsu, Gravitational Wave from Axion-SU(2) Gauge Fields: Effective Field Theory for Kinetically Driven Inflation, arXiv:2004.04350 [INSPIRE].
R. D. Peccei and H. R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2112.07645
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Adshead, P., Lozanov, K.D. Axion anomalies. J. High Energ. Phys. 2022, 77 (2022). https://doi.org/10.1007/JHEP08(2022)077
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)077