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Erratum to: Classification of non-Riemannian doubled-yet-gauged spacetime

  • Kevin Morand
  • Jeong-Hyuck Park
Open Access
Erratum

1 Erratum to: Eur. Phys. J. C (2017) 77:685  https://doi.org/10.1140/epjc/s10052-017-5257-z

Equation (2.51) in the original article as well as the arXiv versions [v1, v2, v3] contains sign errors. It should read
$$\begin{aligned} Y_{i}^{\mu }\longmapsto & {} Y_{i}^{\mu }+H^{\mu \nu }V_{\nu i}\,,\\ {\bar{Y}}_{\bar{\imath }}^{\mu }\longmapsto & {} {\bar{Y}}_{\bar{\imath }}^{\mu } +H^{\mu \nu }{\bar{V}}_{\nu \bar{\imath }}\,,\\ k_{\mu }{}^{a}\longmapsto & {} k_{\mu }{}^{a}-X_{\mu }^{i}\eta ^{ab}h_{b}{}^{\nu }V_{\nu i} -{\bar{X}}_{\mu }^{\bar{\imath }}\eta ^{ab}h_{b}{}^{\nu }{\bar{V}}_{\nu \bar{\imath }}\,,\\ {\bar{k}}_{\mu }{}^{\bar{a}}\longmapsto & {} {\bar{k}}_{\mu }{}^{\bar{a}} +X_{\mu }^{i}\bar{\eta }^{\bar{a}\bar{b}}\bar{h}_{\bar{b}}{}^{\nu }V_{\nu i}+{\bar{X}}_{\mu }^{\bar{\imath }}\bar{\eta }^{\bar{a}\bar{b}}\bar{h}_{\bar{b}}{}^{\nu }{\bar{V}}_{\nu \bar{\imath }}\,,\\ B_{\mu \nu }\longmapsto & {} B_{\mu \nu } -2X^{i}_{[\mu }V_{\nu ]i} +2{\bar{X}}^{\bar{\imath }}_{[\mu }{\bar{V}}_{\nu ]\bar{\imath }}\\&+2X^{i}_{[\mu }{\bar{X}}^{\bar{\imath }}_{\nu ]}\left( Y_{i}^{\rho }{\bar{V}}_{\rho \bar{\imath }} +{\bar{Y}}_{\bar{\imath }}^{\rho }V_{\rho i}+V_{\rho i}H^{\rho \sigma }{\bar{V}}_{\sigma \bar{\imath }}\right) \,. \end{aligned}$$
Under these transformations, the DFT-vielbeins are invariant up to twofold local Lorentz rotations.

K. Morand, J.H. Park, Classification of non-Riemannian doubled-yet-gauged spacetime. Eur. Phys. J. C 77(10), 685 (2017).  https://doi.org/10.1140/epjc/s10052-017-5257-z. arXiv:1707.03713 [hep-th]

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© The Author(s) 2018

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Authors and Affiliations

  1. 1.Departamento de Ciencias FísicasUniversidad Andres BelloSantiago de ChileChile
  2. 2.Departamento de FísicaUniversidad Técnica Federico Santa María, Centro Científico-Tecnológico de ValparaísoValparaísoChile
  3. 3.Department of PhysicsSogang UniversitySeoulKorea
  4. 4.Center for Theoretical Physics of the UniverseInstitute for Basic Science (IBS)SeoulKorea

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