Effective Field Theory for Quantum Gravity from ... - Relativity Group

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Construction of Doubly General Relativity (I)Extending Shape Dynamicsfixed CMC condition Q(x) = π(x) + λ √ |g|conformal spatial harmonic gaugeF k (x) = (g ab δ k c + 1 3 g ak δ b c )e c α(∇ a − ˆ∇ a )e α bFirst class system: {Q(x), Q(y)} = 0 = {F i (x), F j (y)}as well as {Q(x), F i (y)} = F i (y)δ(x, y)Interpretation as “local conformal system”Q generates spatial dilatations and Poisson brackets resemble C(3) ateach pointGauge fixing ADMgauge fixing operator is elliptic and invertible in a region Rout side R: meager set with finite dimensional kernelT. Koslowski (PI) Quantum Shape Dynamics April 10th, 2012 12 / 23
Construction of Doubly General Relativity (II)BRST-chargesΩ ADM = ∫ ()d 3 x ηS + η a g ac π;d cd + ηb η,b a P a + 1 2 ηa η ,a P + ηη ,c P b g bcΩ ESD = ∫ ()d 3 x P √ π g+ P a F a + 1 P√2 gP a η aGauge-fixed gravity actionS gf = ∫ dt (symp.pot. + {Ω ADM , Ω ESD }) is invariant under usualADM-BRST transformations anda hidden BRST-invariance of S gfunders ESD g ab = P √ gg ab s ESD π ab = “long ′′s ESD η = − √ 1g(π + 1 2 P cη c ) s ESD P = 0s ESD η a = −F a + P2 √ g ηa s ESD P a = P2 √ g P adue to extended Shape Dynamics.T. Koslowski (PI) Quantum Shape Dynamics April 10th, 2012 13 / 23
Page 2 and 3: OutlineIntroduction: motivation, go
Page 4 and 5: Main Message“Doubly General Relat
Page 6 and 7: Symmetry Trading MechanismT. Koslow
Page 8 and 9: Relation of Dirac ObservablesInters
Page 10 and 11: DOUBLY GENERAL RELATIVITYsymmetry d
Page 14 and 15: Construction of Doubly General Rela
Page 16 and 17: Renormalization Group and Effective
Page 18 and 19: FURTHER DIRECTIONSdualities, experi
Page 20 and 21: Bulk/bulk dualityUsual Shape Dynami
Page 22 and 23: Conclusions1 Symmetry trading is ge

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