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Chern-Simons Extension of ESK Theory

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 Added by Luca Fabbri
 Publication date 2020
  fields Physics
and research's language is English
 Authors Luca Fabbri




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The commonly-known Chern-Simons extension of Einstein gravitational theory is written in terms of a square-curvature term added to the linear-curvature Hilbert Lagrangian. In a recent paper, we constructed two Chern-Simons extensions according to whether they consisted of a square-curvature term added to the square-curvature Stelle Lagrangian or of one linear-curvature term added to the linear-curvature Hilbert Lagrangian [Ref. 4]. The former extension gives rise to the topological extension of the re-normalizable gravity, the latter extension gives rise to the topological extension of the least-order gravity. This last theory will be written here in its torsional completion. Then a consequence for cosmology and particle physics will be addressed.



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87 - Luca Fabbri 2020
We write the most general parity-even re-normalizable Chern-Simons term for massive axial-vector propagating torsion fields. After obtaining the most comprehensive action, we perform the causal structure analysis to see what self-interaction term must be suppressed. In view of such a restriction for the Lagrangian, we will obtain the field equations, investigating some of their properties.
124 - Brendan McLellan 2012
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. A symplectic abelian Chern-Simons partition function is also derived using the technique of non-abelian localization. This physically identifies the symplectic abelian partition function with the abelian Chern-Simons partition function as rigorous topological three-manifold invariants. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three-manifolds. The torsion part of the abelian Chern-Simons partition function is computed explicitly in terms of Seifert data for a given Sasakian three-manifold.
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