Schwinger limit



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In quantum electrodynamics and quantum chromodynamics the Schwinger limit is a maximal scale

m 2c 3e \;\approx\; \frac{ m^2 c^3 }{ e \hbar }

of the field strength of an electric background field beyond which the vacuum polarization caused by pair creation electrons/positrons or quarks/anti-quarks (of charge ee and mass mm) out of the vacuum, via the Schwinger effect, becomes sizeable, leading to non-linearities and/or vacuum decay.

From the perspective of geometric engineering of QCD in intersecting D-brane models (holographic QCD) the Schwinger limit corresponds to the limiting field strength in the DBI-action of the Chan-Paton gauge field on D-branes (“holographic Schwinger effect”).

The Schwinger effect and its resulting Schwinger limit are securely prediuted by established quantum field theory, but have not been observed in experiment yet. However, recent experiments are getting very close and upcoming experiments might see the effect.


From the rate

(1)Γ=e 28π 2n=11ncoth(nπ)exp(m 2πne) \Gamma \;=\; \frac { e^2 \mathcal{E} \mathcal{B} }{ 8 \pi^2 } \underoverset {n = 1} {\infty} {\sum} \frac{1}{n} \coth \left( \frac{\mathcal{B}}{\mathcal{E}} n \pi \right) \exp \left( - \frac{ m^2 \pi n }{ e \mathcal{E} } \right)

(here) of particle pair creation via the Schwinger effect one deduces a critical electric field strength crit\mathcal{E}_{crit} which sets the scale beyond which the vacuum polarization due to the Schwinger effect counteracts the ambient electric field and/or leads to vacuum decay.

As a Lorentz invariant (here) this Schwinger limit for the electric field strength is:

(2) critm 2c 3e \mathcal{E}_{crit} \;\coloneqq\; \frac{ m^2 c^3 }{ e \hbar }

(Dunne 04, (1.3), Martin 07, (40))


This is such that the corresponding Lorentz force

F crite crit F_{crit} \; \coloneqq \; e \, \mathcal{E}_{crit}

acting over the Compton wavelength λ Compmc\lambda_{Comp} \;\coloneqq\; \frac{\hbar }{m c} equals the rest energy mc 2m c^2 of the given charged particle:

F critλ Comp=mc 2 crit=mc 2eλ Comp \begin{aligned} & F_{crit} \lambda_{Comp} \; = \; m c^2 \\ \Leftrightarrow \;\;\; & \mathcal{E}_{crit} \; = \; \frac{ m c^2 }{ e \lambda_{Comp} } \end{aligned}


Relation to DBI-limit

Expressing (2) in terms of the corresponding critical value E critE_{crit} of the actual electric field strength (here) in the given Lorentz frame yields (Hashimoto-Oka-Sonoda 14b, (2.17), check):

(E crit,B)= critAAAAE crit= crit crit 2+B 2 crit 2+B 2 \mathcal{E}(E_{crit}, B) \;=\; \mathcal{E}_{crit} \phantom{AA} \Leftrightarrow \phantom{AA} E_{crit} \;=\; \mathcal{E}_{crit} \sqrt{ \frac{ \mathcal{E}_{crit}^2 + B^2 } { \mathcal{E}_{crit}^2 + B_{\parallel}^2 } }

This happens to coincide with the critical field strength of the DBI-action, see there.

fundamental scales (fundamental physical units)




For more see the references at Schwinger effect.

See also

Experimental realization

Discussion of experiments that could/should see physics at the Schwinger limit:

  • Gerald Dunne, New Strong-Field QED Effects at ELI: Nonperturbative Vacuum Pair Production, Eur. Phys. J. D55:327-340, 2009 (arXiv:0812.3163)

  • Hidetoshi Taya, Mutual assistance between the Schwinger mechanism and the dynamical Casimir effect (arXiv:2003.12061)

  • Florian Hebenstreit, A space-time resolved view of the Schwinger effect, Frontiers of intense laser physics – KITP 2014 (pdf)

Holographic Schwinger effect

Interpretation in holographic QCD of the Schwinger effect of vacuum polarization as exhibited by the DBI-action on flavor branes:

Precursor computation in open string theory:

Relation to the DBI-action of a probe brane in AdS/CFT:

  • Gordon Semenoff, Konstantin Zarembo, Holographic Schwinger Effect, Phys. Rev. Lett. 107, 171601 (2011) (arXiv:1109.2920, doi:10.1103/PhysRevLett.107.171601)

  • S. Bolognesi, F. Kiefer, E. Rabinovici, Comments on Critical Electric and Magnetic Fields from Holography, J. High Energ. Phys. 2013, 174 (2013) (arXiv:1210.4170)

  • Yoshiki Sato, Kentaroh Yoshida, Holographic description of the Schwinger effect in electric and magnetic fields, J. High Energ. Phys. 2013, 111 (2013) (arXiv:1303.0112)

  • Yoshiki Sato, Kentaroh Yoshida, Holographic Schwinger effect in confining phase, JHEP 09 (2013) 134 (arXiv:1306.5512

  • Yoshiki Sato, Kentaroh Yoshida, Universal aspects of holographic Schwinger effect in general backgrounds, JHEP 12 (2013) 051 (arXiv:1309.4629)

  • Daisuke Kawai, Yoshiki Sato, Kentaroh Yoshida, The Schwinger pair production rate in confining theories via holography, Phys. Rev. D 89, 101901 (2014) (arXiv:1312.4341)

  • Yue Ding, Zi-qiang Zhang, Holographic Schwinger effect in a soft wall AdS/QCD model (arXiv:2009.06179)

Relation to DBI-action of flavor branes in holographic QCD:

See also:

  • Xing Wu, Notes on holographic Schwinger effect, J. High Energ. Phys. 2015, 44 (2015) (arXiv:1507.03208, doi:10.1007/JHEP09(2015)044)

  • Kazuo Ghoroku, Masafumi Ishihara, Holographic Schwinger Effect and Chiral condensate in SYM Theory, J. High Energ. Phys. 2016, 11 (2016) (doi:10.1007/JHEP09(2016)011)

  • Le Zhang, De-Fu Hou, Jian Li, Holographic Schwinger effect with chemical potential at finite temperature, Eur. Phys. J. A54 (2018) no.6, 94 (spire:1677949, doi:10.1140/epja/i2018-12524-4)

  • Wenhe Cai, Kang-le Li, Si-wen Li, Electromagnetic instability and Schwinger effect in the Witten-Sakai-Sugimoto model with D0-D4 background, Eur. Phys. J. C 79, 904 (2019) (doi:10.1140/epjc/s10052-019-7404-1)

  • Zhou-Run Zhu, De-fu Hou, Xun Chen, Potential analysis of holographic Schwinger effect in the magnetized background (arXiv:1912.05806)

  • Zi-qiang Zhang, Xiangrong Zhu, De-fu Hou, Effect of gluon condensate on holographic Schwinger effect, Phys. Rev. D 101, 026017 (2020) (arXiv:2001.02321)


  • Daisuke Kawai, Yoshiki Sato, Kentaroh Yoshida, A holographic description of the Schwinger effect in a confining gauge theory, International Journal of Modern Physics A Vol. 30, No. 11, 1530026 (2015) (arXiv:1504.00459)

  • Akihiko Sonoda, Electromagnetic instability in AdS/CFT, 2016 (spire:1633963, pdf)

Last revised on April 5, 2020 at 10:12:48. See the history of this page for a list of all contributions to it.