Abstract
We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric fields and result in configurations with linking numbers, which can be characterized by non-invertible global symmetries. The so-called chiral plasma instability and instabilities of the axion electrodynamics and (4 + 1)-dimensional Maxwell-Chern-Simons theory in electric fields can be described by the generalized chiral instabilities in a unified manner. We also illustrate this mechanism in the (2+1)-dimensional Goldstone-Maxwell model in electric field.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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 [INSPIRE].
M.M. Anber and L. Sorbo, N-flationary magnetic fields, JCAP 10 (2006) 018 [astro-ph/0606534] [INSPIRE].
M. Joyce and M.E. Shaposhnikov, Primordial magnetic fields, right-handed electrons, and the Abelian anomaly, Phys. Rev. Lett. 79 (1997) 1193 [astro-ph/9703005] [INSPIRE].
Y. Akamatsu and N. Yamamoto, Chiral Plasma Instabilities, Phys. Rev. Lett. 111 (2013) 052002 [arXiv:1302.2125] [INSPIRE].
O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Striped instability of a holographic Fermi-like liquid, JHEP 10 (2011) 034 [arXiv:1106.3883] [INSPIRE].
H. Ooguri and M. Oshikawa, Instability in magnetic materials with dynamical axion field, Phys. Rev. Lett. 108 (2012) 161803 [arXiv:1112.1414] [INSPIRE].
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
K. Kamada, N. Yamamoto and D.-L. Yang, Chiral effects in astrophysics and cosmology, Prog. Part. Nucl. Phys. 129 (2023) 104016 [arXiv:2207.09184] [INSPIRE].
P.A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge University Press (2001) [https://doi.org/10.1017/cbo9780511626333].
C. Cordova, T.T. Dumitrescu, K. Intriligator and S.-H. Shao, Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond, in proceedings of the Snowmass 2021, Seattle, WA, U.S.A., 17–26 July 2022, arXiv:2205.09545 [INSPIRE].
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].
Y. Choi, H.T. Lam and S.-H. Shao, Noninvertible Global Symmetries in the Standard Model, Phys. Rev. Lett. 129 (2022) 161601 [arXiv:2205.05086] [INSPIRE].
C. Cordova and K. Ohmori, Noninvertible Chiral Symmetry and Exponential Hierarchies, Phys. Rev. X 13 (2023) 011034 [arXiv:2205.06243] [INSPIRE].
Y. Choi, H.T. Lam and S.-H. Shao, Non-invertible Gauss Law and Axions, arXiv:2212.04499 [INSPIRE].
R. Yokokura, Non-invertible symmetries in axion electrodynamics, arXiv:2212.05001 [INSPIRE].
P. Putrov and J. Wang, Categorical Symmetry of the Standard Model from Gravitational Anomaly, arXiv:2302.14862 [INSPIRE].
I. García Etxebarria and N. Iqbal, A Goldstone theorem for continuous non-invertible symmetries, arXiv:2211.09570 [INSPIRE].
A. Karasik, On anomalies and gauging of U(1) non-invertible symmetries in 4d QED, arXiv:2211.05802 [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
N. Yamamoto and R. Yokokura, Unstable Nambu-Goldstone modes, Phys. Rev. D 106 (2022) 105004 [arXiv:2203.02727] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications. Part I, SciPost Phys. 8 (2020) 001 [arXiv:1905.09315] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications. Part II, SciPost Phys. 8 (2020) 002 [arXiv:1905.13361] [INSPIRE].
A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].
H.B. Nielsen and M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. B 130 (1983) 389 [INSPIRE].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
N. Sogabe and N. Yamamoto, Triangle Anomalies and Nonrelativistic Nambu-Goldstone Modes of Generalized Global Symmetries, Phys. Rev. D 99 (2019) 125003 [arXiv:1903.02846] [INSPIRE].
Y. Hidaka, M. Nitta and R. Yokokura, Higher-form symmetries and 3-group in axion electrodynamics, Phys. Lett. B 808 (2020) 135672 [arXiv:2006.12532] [INSPIRE].
Y. Hidaka, M. Nitta and R. Yokokura, Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics, JHEP 01 (2021) 173 [arXiv:2009.14368] [INSPIRE].
H.K. Moffatt, The degree of knottedness of tangled vortex lines, J. Fluid Mech. 35 (1969) 117.
X. Chen, A. Tiwari and S. Ryu, Bulk-boundary correspondence in (3 + 1)-dimensional topological phases, Phys. Rev. B 94 (2016) 045113 [Addendum ibid. 94 (2016) 079903] [arXiv:1509.04266] [INSPIRE].
Y. Akamatsu and N. Yamamoto, Chiral Langevin theory for non-Abelian plasmas, Phys. Rev. D 90 (2014) 125031 [arXiv:1402.4174] [INSPIRE].
J.A. Damia, R. Argurio and E. Garcia-Valdecasas, Non-invertible defects in 5d, boundaries and holography, SciPost Phys. 14 (2023) 067 [arXiv:2207.02831] [INSPIRE].
E. García-Valdecasas, Non-invertible symmetries in supergravity, JHEP 04 (2023) 102 [arXiv:2301.00777] [INSPIRE].
P. Sikivie, On the Interaction of Magnetic Monopoles With Axionic Domain Walls, Phys. Lett. B 137 (1984) 353 [INSPIRE].
F. Wilczek, Two Applications of Axion Electrodynamics, Phys. Rev. Lett. 58 (1987) 1799 [INSPIRE].
X.-L. Qi, T. Hughes and S.-C. Zhang, Topological Field Theory of Time-Reversal Invariant Insulators, Phys. Rev. B 78 (2008) 195424 [arXiv:0802.3537] [INSPIRE].
A.M. Essin, J.E. Moore and D. Vanderbilt, Magnetoelectric polarizability and axion electrodynamics in crystalline insulators, Phys. Rev. Lett. 102 (2009) 146805 [arXiv:0810.2998] [INSPIRE].
C. Córdova, T.T. Dumitrescu and K. Intriligator, Exploring 2-Group Global Symmetries, JHEP 02 (2019) 184 [arXiv:1802.04790] [INSPIRE].
J.A. Damia, R. Argurio and L. Tizzano, Continuous Generalized Symmetries in Three Dimensions, JHEP 23 (2023) 164 [arXiv:2206.14093] [INSPIRE].
Acknowledgments
N.Y. is supported in part by the Keio Institute of Pure and Applied Sciences (KiPAS) project at Keio University and JSPS KAKENHI Grant Numbers JP19K03852 and JP22H01216. R.Y. is supported by JSPS KAKENHI Grants Numbers JP21K13928 and JP22KJ3120.
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: 2305.01234
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
Yamamoto, N., Yokokura, R. Generalized chiral instabilities, linking numbers, and non-invertible symmetries. J. High Energ. Phys. 2023, 45 (2023). https://doi.org/10.1007/JHEP07(2023)045
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2023)045