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Induced gravitational topological term and the Einstein-Cartan modified theory

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J. R. Nascimento, A. Yu. Petrov, P. J. Porfírio

General Relativity and Quantum Cosmology · Submitted 12 Aug 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim However, in particular, we find a non-trivial solution where the modified field equations do not reduce to the GR ones.

how it is stated · asserted 1.00 read the record →

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arXiv ID2108.05705 (version 4)
Pith IDI6Y32W6W, Pith's permanent record of this paper and its review
CitationA. Yu. Petrov, J. R. Nascimento, P. J. Porf\'irio. "Induced gravitational topological term and the Einstein-Cartan modified theory." arXiv:2108.05705 (2021). https://pith.science/paper/I6Y32W6W
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,929 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.33 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

It is well known that only the axial piece of the torsion couples minimally to fermions in a Riemann-Cartan geometry, while the other ones decouple. In this paper, we consider the Dirac field minimally coupled to a dynamical background with torsion and compute its contribution to the fermionic one-loop effective action. Such a contribution owns topological nature since it can be linked with topological invariants from Riemann-Cartan spaces, like Nieh-Yan and Chern-Simons terms. Furthermore, we propose a novel modified theory of gravity constructed by adding the aforementioned one-loop contribution to the Einstein-Cartan action. The modified field equations reduce to those ones of GR under certain circumstances, providing therefore trivial solutions. However, in particular, we find a non-trivial solution where the modified field equations do not reduce to the GR ones.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 It is well known that only the axial piece of the torsion couples minimally to fermions in a Riemann-Cartan geometry, while the other ones decouple. background 1.00 0.03 0.03 asserted 1.00
s1 In this paper, we consider the Dirac field minimally coupled to a dynamical background with torsion and compute its contribution to the fermionic one-loop effective action. contribution 0.86 0.95 0.04 asserted 0.96
s2 Such a contribution owns topological nature since it can be linked with topological invariants from Riemann-Cartan spaces, like Nieh-Yan and Chern-Simons terms. interpretation 0.52 0.71 0.11 asserted 0.98
s3 Furthermore, we propose a novel modified theory of gravity constructed by adding the aforementioned one-loop contribution to the Einstein-Cartan action. contribution 0.99 0.93 0.25 asserted 0.98
s4 The modified field equations reduce to those ones of GR under certain circumstances, providing therefore trivial solutions. result 0.94 0.79 0.08 asserted 0.97
s5 However, in particular, we find a non-trivial solution where the modified field equations do not reduce to the GR ones. result 1.00 0.96 0.51 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

It is well known that only the axial piece of the torsion couples minimally to fermions in a Riemann-Cartan geometry, while the other ones decouple. In this paper, we consider the Dirac field minimally coupled to a dynamical background with torsion and compute its contribution to the fermionic one-loop effective action. Such a contribution owns topological nature since it can be linked with topological invariants from Riemann-Cartan spaces, like Nieh-Yan and Chern-Simons terms. Furthermore, we propose a novel modified theory of gravity constructed by adding the aforementioned one-loop contribution to the Einstein-Cartan action. The modified field equations reduce to those ones of GR under certain circumstances, providing therefore trivial solutions. However, in particular, we find a non-trivial solution where the modified field equations do not reduce to the GR ones.

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References
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5 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

Cites it as background 1 paper

What it cites · 24 sentences without a confident label

Uses the method or tool of 1 paper
  • Upon carrying out the trace over the Dirac gamma matrices and integration over the proper time $s$ (the step-by-step calculation can be made similarly to [ref] ), we obtain the first contribution to the desired effective action: Γ_NY,2 = 1/216π^2∫d^4x√(-g) ϵ^μνλρS_μ∂_νω̃_λabω̃_ρ^ab.

    Lorentz violation and the proper-time method · ONE-LOOP INDUCED GRAVITATIONAL TOPOLOGICAL TERM · 0.96

Compares with 4 papers
  • Apart from that, the divergence of Eq. ([ref]) imposes another constraint or consistency condition to hold the diffeomorphism invariance of the modified theory [equation] which is somewhat similar to the Pontryagin constraint in CSMGR [ref] .

    Chern-Simons Modification of General Relativity · EINSTEIN-CARTAN MODIFIED THEORY WITH ADDITIVE TOPOLOGICAL TERM · 0.96

  • In particular, Schwarzschild metric persists as a solution of our EC modified theory, in contrast to the modified theory proposed in [ref] .

    Einstein-Cartan formulation of Chern-Simons Lorentz-violating Gravity · EINSTEIN-CARTAN MODIFIED THEORY WITH ADDITIVE TOPOLOGICAL TERM · 0.99

  • It is worth to mention that this novel contact term resembles the interaction term proposed within the non-dynamical version of CSMGR [ref] , with the axial-vector torsion background field playing the role of the axial vector field $v_μ$ defined in those papers.

    Chern-Simons Modified General Relativity · ONE-LOOP INDUCED GRAVITATIONAL TOPOLOGICAL TERM · 1.00

Cites as background 9 papers
  • The tensor $X_μν$ is sometimes called the Cotton tensor [ref] .

    Chern-Simons Modification of General Relativity · EINSTEIN-CARTAN MODIFIED THEORY WITH ADDITIVE TOPOLOGICAL TERM · 0.80

  • First, let us begin exhibiting the Dirac action minimally coupled to gravity and torsion in a Riemann-Cartan background [ref] [equation] where $γ^a$ is the usual flat-space Dirac matrices and $e^a_ μ$ is the vierbein field.

    Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion · Fermions in a Riemann-Cartan space · 0.90

  • First, let us begin exhibiting the Dirac action minimally coupled to gravity and torsion in a Riemann-Cartan background [ref] [equation] where $γ^a$ is the usual flat-space Dirac matrices and $e^a_ μ$ is the vierbein field.

    Physical Aspects of the Space-Time Torsion · Fermions in a Riemann-Cartan space · 0.90

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