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Extended solution space for Chern-Simons gravity

Extended solution space for Chern-Simons gravity

Chern-Simons (CS) term and LV• CPT theorem: Local Lorentz invariant quantum field theories ⇒ CPT invariance.Their breakdown should be related too. . . ???• Greenberg, PRL (2002) demonstrated it. “Basically” stating that CPT violation impliedLorentz violation• Carroll’s et al. extension of electrodynamics was actually due to a CPT -odd term(∼ ⃗ A · ⃗B) of the CS form, where gauge invariance was retained at the price of havingLV.Will focus on extensions of the CS kindVIII Silafae - UTFSM, Valparaíso, 2010 Mauro Cambiaso New solutions in Chern-Simons gravity – p. 4

Extension of gravity by CS term• Appealing mathematical properties, CS → related to topological invariants.• CS modified gravity → Gravitational parity-violation, motivated, eg. by anomaly cancellationin Particle Physics, Alexander, Phys. Repts (2009) .• Natural in the gauge theory approach to gravity (PGT), so would the Holst or Nieh-Yan terms.• In QED for example, fermion loops by a LV axion-like vector ∼ b µ ¯ψ γ5 γ µ ψ could generatethe CS term in the photon sector.In GR the CS-like term can be understood as due to radiative loops of fermions coupled to anaxial inflaton ∼ b µ γ 5 . Lue, PRL, (1999).Will focus on GR extended by a CS term.VIII Silafae - UTFSM, Valparaíso, 2010 Mauro Cambiaso New solutions in Chern-Simons gravity – p. 5

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