Quantum Gravity and the Renormalization Group

Transcription

1 Nicolai Christiansen (ITP Heidelberg) Schladming Winter School 2013 Quantum Gravity and the Renormalization Group Partially based on: arxiv: [hep-th] (NC,Litim,Pawlowski,Rodigast) and work in progress by N.Christiansen, J.M. Pawlowski, A. Rodigast

2 Outline 1. Introduction 2. The Asymptotic Safety Scenario 3. Results: Fixed Point Structure (UV - IR) Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

3 Classical Gravity classical gravity is described by general relativity on all scales observed so far Einstein Hilbert action no precision tests dark matter?! dimensional analysis: Newtons Constant Ricci Scalar Cosmological Constant Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

4 Perturbative Quantization relevant energy scale: Planck Scale, perturbative expansion parameter for n-point Greens functions: dimensionless energy scale higher loop orders require higher derivative counterterms! full theory is either divergent or includes infinitely many free parameters (perturbatively) non-renormalizable Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

5 Quantum Gravity and UV completion for energy scales effective field theory UV completion? String Theory Loop Quantum Gravity... perturbation theory as the root of all problems? stick to framework of ordinary QFT non-perturbative construction Asymptotic Safety Scenario (Weinberg, 79) based on non-trivial UV fixed point Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

6 The Asymptotic Safety Scenario construct quantum gravity via a path integral formulation: (a) d.o.f carried by the metric tensor field (b) diffeomorphism invariance quantum fluctuations scale dependent couplings all possible couplings energy scale UV fixed point: finite fixed point value finite number of free parameters (predictive!) Asymptotic Safety Special case: Asymptotic Freedom Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

7 The Asymptotic Safety Scenario calculate non-perturbative RG flow of the couplings (non-perturbative beta-functions) Functional Renormalization Group (lecture J.Pawlowski) fully dressed propagator scale dependent effective action regulator Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

8 The Asymptotic Safety Scenario the full effective action contains in principle infinitely many couplings / operators truncations Standard Truncation: Einstein-Hilbert Truncation scale dependence, Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

9 The Asymptotic Safety Scenario UV fixed point is well established in various approximations, e.g. : (1) four derivative operators (2) f(r) gravity: (3) coupling to matter / gauge fields up to n=34! ( ) the deep infrared has been problematic: singularity in the IR UV fixed point infrared catastrophe! Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

10 The Asymptotic Safety Scenario improved setup: flow of the propagator graviton field cosmological constant: Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

11 Results I UV fixed point IR fixed point Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

12 Results II flow of the coupling flow of the cosmological constant UV fixed point UV fixed point IR fixed point IR scaling Classical General Relativity for Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

13 Results II flow of the coupling flow of the cosmological constant UV fixed point UV fixed point IR fixed point IR scaling Classical General Relativity for Nicolai Christiansen (ITP Heidelberg), Schladming Winter School

14 Summary finite and predictive theory of quantum gravity: Asymptotic Safety Scenario enhanced Einstein Hilbert Truncation UV fixed point IR fixed point with Classical General Relativity Thank you for your attention Nicolai Christiansen (ITP Heidelberg), Schladming Winter School