Erratum: Einstein-Cartan gravity, matter, and scale-invariant generalization

JHEP08(2021)162

Published for SISSA by Springer Received: August 9, 2021 Accepted: August 10, 2021 Published: August 30, 2021

Erratum: Einstein-Cartan gravity, matter, and scale-invariant generalization

M. Shaposhnikov, A. Shkerin, I. Timiryasov and S. Zell Institue of Physics, Laboratory for Particle Physics and Cosmology,

École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland E-mail: mikhail.shaposhnikov@epfl.ch,andrey.shkerin@epfl.ch, inar.timiryasov@epfl.ch,sebastian.zell@epfl.ch

Erratum to: JHEP10(2020)177

ArXiv ePrint: 2007.16158

• Contrary to the claim made after eq. (2.14), the fermionic action (2.6) is not invariant under the transformation (2.10) supplemented with Ψ7→Ω^3/2Ψ. Instead, it transforms as follows:

S_f 7→S_f +1 8

Z _{IJ KL}e^Ie^Je^KdΩ²

Ω² (αV^L+βA^L), whereV^L and A^L are defined in eq. (2.17).

• Eq. (2.18) should read

−2C^[I_KB^J]K+ dη

Ω² + dγ

e^Ie^J

= 1 M_P²

1

2e^Ie^Je^PA_P +1

6_{KLM N}e^Ke^Le^Mδ^N[IαV^J]+βA^J]

.

• Eq. (2.21) should read S^eff =

Z d⁴x√

−g (M_P²

2

R˚+ i

2Ψγ^µD˚µΨ− i 2

D˚µΨγ^µΨ )

− Z

d⁴x√

−g 1

2Ω²(∂µh)²+ U Ω⁴

− Z

d⁴x√

−g 3M_P² 4(γ²+ 1)

∂µη Ω² +∂µγ

2

+ Z

d⁴x√

−g3α 4

∂_µΩ² Ω² + γ

γ²+ 1 ∂_µη

Ω² +∂µγ !

V^µ

+ Z

d⁴x√

−g3

4 β∂_µΩ²

Ω² +1 +γβ γ²+ 1

∂_µη Ω² +∂_µγ

! A^µ

− Z

d⁴x√

−g 3 16M_P²(γ²+ 1)

1 + 2γβ−β²A²_µ+ 2α(γ−β)A_µV^µ−α²V_µ². This change does not affect any discussions in the paper.

Open Access, cThe Authors.

Article funded by SCOAP³. https://doi.org/10.1007/JHEP08(2021)162

JHEP08(2021)162

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.

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