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Extended solution space for Chern-Simons gravity

Extended solution space for Chern-Simons gravity

Jackiw & Pi’s version

Jackiw & Pi’s version of EH + CS• The model is described by the following action:S EH+CS [g] = 116πG∫d 4 x ( √ −g R − 1 4 ϑ ∗ RR )where v µ is an embedding vector and the CS current defined as:[K µ = ǫ µαβγ Γ σ ατ ∂ β Γ τ γσ + 2 ]3 Γσ ατ Γ τ βη Γη γσand∂ µ K µ = 2 ∗ RR.Integrating by parts with ∂ µ ϑ ≡ v µ .• ONLY dynamical variable: g µν . Γ µ αβ→ Levi-Cività connection.• ∴ Demanding the space of solutions of this theory to be torsion-free.VIII Silafae - UTFSM, Valparaíso, 2010 Mauro Cambiaso New solutions in Chern-Simons gravity – p. 6

Jackiw & Pi’s version of EH + CS• The model is described by the following action:S EH+CS [g] = 116πG∫d 4 x ( √ −g R − 1 4 ϑ ∗ RR )where v µ is an embedding vector and the CS current defined as:[K µ = ǫ µαβγ Γ σ ατ ∂ β Γ τ γσ + 2 ]3 Γσ ατ Γ τ βη Γη γσand∂ µ K µ = 2 ∗ RR.Integrating by parts with ∂ µ ϑ ≡ v µ .• ONLY dynamical variable: g µν . Γ µ αβ→ Levi-Cività connection.• ∴ Demanding the space of solutions of this theory to be torsion-free.• The gravitational CS current above is akin to the one of non-Abelian gauge theoriesA ∧ dA + 2 3 A ∧ A ∧ A.VIII Silafae - UTFSM, Valparaíso, 2010 Mauro Cambiaso New solutions in Chern-Simons gravity – p. 6

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