Advertisement

Erratum to: Emergent gauge bosons and dynamical symmetry breaking in a four-fermion Lifshitz model

  • T. Mariz
  • R. Moreira
  • A. Yu. PetrovEmail author
Open Access
Erratum

1 Erratum to: Eur. Phys. J. C (2019) 79:550 https://doi.org/10.1140/epjc/s10052-019-7068-x

In this Erratum we correct some numerical coefficients for the low-energy effective action we obtained in our paper [1].
  1. 1.
    The Eq. (37) must be read as:
    $$\begin{aligned} \mathcal{L}_\mathrm {eff}= & {} \frac{g_t^2}{2}A_0A^0 -\frac{{{\tilde{\alpha }}}_2}{2} \left( \partial _0A_i\partial ^0A^i-\frac{6}{5}\partial _0A_i\partial ^iA^0\nonumber \right. \\&\left. -\frac{6}{5}\partial _iA_0\partial ^0A^i+\frac{36}{25}\partial _iA_0\partial ^iA^0 \right) \nonumber \\&-\frac{{{\tilde{\alpha }}}_5m^4}{2}(\partial _iA_j\partial ^iA^j-\partial _iA_j\partial ^jA^i)\nonumber \\&-\frac{9{{\tilde{\alpha }}}_2}{50}\partial _iA_0\partial ^iA^0-\frac{{{\tilde{\beta }}} m^4e^2}{4}\left( A_iA^i-\frac{a_ia^i}{e^2}\right) ^2,\nonumber \\ \end{aligned}$$
    (37)
     
  2. 2.
    The Eqs. (41–44) must be read as:
    $$\begin{aligned} A_0\rightarrow & {} \frac{5m{{\tilde{\alpha }}}_5^{1/4}}{6{{\tilde{\alpha }}}_2^{1/2}}A_0, \end{aligned}$$
    (41a)
    $$\begin{aligned} A_i\rightarrow & {} \frac{1}{m{{\tilde{\alpha }}}_5^{1/4}}A_i, \end{aligned}$$
    (41b)
    $$\begin{aligned} \partial _0\rightarrow & {} \frac{m^2{{\tilde{\alpha }}}_5^{1/4}}{{{\tilde{\alpha }}}_2^{1/2}}\partial _0, \end{aligned}$$
    (41c)
    $$\begin{aligned} \partial _i\rightarrow & {} \frac{1}{{{\tilde{\alpha }}}_5^{1/4}}\partial _i, \end{aligned}$$
    (41d)
     
$$\begin{aligned} \mathcal{L}_\mathrm {eff}= & {} -\frac{m^2}{4}F_{\mu \nu }F^{\mu \nu } -\frac{m^2}{8}(\partial _iA_0)^2 +\frac{g_t^2}{2}\frac{25m^2{{\tilde{\alpha }}}_5^{1/2}}{36{{\tilde{\alpha }}}_2}A_0A^0\nonumber \\&-\frac{{{\tilde{\beta }}} m^2e^2}{4{{\tilde{\alpha }}}_5}\left( A_iA^i-\frac{a_ia^i}{e^2}\right) ^2. \end{aligned}$$
(42)
$$\begin{aligned} \mathcal{L}_\mathrm {eff}= & {} -\frac{m^2}{4}F_{\mu \nu }F^{\mu \nu } -\frac{{{\tilde{\beta }}} m^2e^2}{4{{\tilde{\alpha }}}_5}\left( A_i A^i-\frac{a_i a^i}{e^2}\right) ^2, \end{aligned}$$
(43)
$$\begin{aligned} \mathcal{L}_{\mathrm {eff}}= & {} -\frac{m^2}{2}F_{0i}F^{0i}+\frac{m^2}{4}F_{ij}F^{ij}\nonumber \\&-\frac{{{\tilde{\beta }}} m^2e^2}{4|{{\tilde{\alpha }}}_5|}\left( A_i A^i-\frac{a_i a^i}{e^2}\right) ^2. \end{aligned}$$
(44)
None of physical conclusions of our paper are changed under these corrections.

Notes

Acknowledgements

This work was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). The work by A. Yu. P. has been partially supported by the CNPq project 303783/2015-0.

Reference

  1. 1.
    T. Mariz, R. Moreira, A.Yu. Petrov, Eur. Phys. J. C 79, 550 (2019)Google Scholar

Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Funded by SCOAP3

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal de AlagoasMaceióBrazil
  2. 2.Departamento de FísicaUniversidade Federal da ParaíbaJoão PessoaBrazil

Personalised recommendations