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Asymptotic Safety in Lorentzian quantum gravity

Edoardo D'Angelo

Abstract

We report on a recently introduced Functional Renormalization Group (RG) Equation, and we apply it to quantum gravity in Lorentzian spacetimes. While the RG flow is state-dependent, it is possible to evaluate state and background independent contributions to the flow. Taking into account only these universal terms, the RG flow exhibits a non-trivial fixed point in the Einstein-Hilbert truncation, providing a mechanism for Asymptotic Safety in Lorentzian quantum gravity.

Asymptotic Safety in Lorentzian quantum gravity

Abstract

We report on a recently introduced Functional Renormalization Group (RG) Equation, and we apply it to quantum gravity in Lorentzian spacetimes. While the RG flow is state-dependent, it is possible to evaluate state and background independent contributions to the flow. Taking into account only these universal terms, the RG flow exhibits a non-trivial fixed point in the Einstein-Hilbert truncation, providing a mechanism for Asymptotic Safety in Lorentzian quantum gravity.
Paper Structure (8 sections, 28 equations, 1 figure)

This paper contains 8 sections, 28 equations, 1 figure.

Table of Contents

  1. Quantum Gravity as a locally covariant QFT
  2. Renormalization Group flow equations
  3. State dependence
  4. Hadamard subtraction and Local Potential Approximation
  5. Einstein-Hilbert truncation
  6. Universal terms and state dependence
  7. Phase diagram
  8. Conclusions

Figures (1)

  • Figure 1: Phase diagram obtained by numerical integration of the $\beta-$functions \ref{['eq:beta-functions-1']}-\ref{['eq:beta-functions-2']}. The solid line is the separatrix, connecting the non-Gaussian fixed point (circle) to the Gaussian one (square); the dashed line denotes the locus where $\eta_{\text{N}}$ diverges.