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The Renormalization Group provides a unifying tool to study quantum gravity approaches: Bridging the gap between microscopic and macroscopic scales, it can be used in two directions in quantum gravity: On the one hand, following the Renormalization Group flow towards high momentum scales allows us to test the consistency of the asymptotic safety scenario for quantum gravity. On the other hand, following the flow towards the infrared, allows us to check whether a viable semiclassical limit emerges from a microscopic model of quantum gravity, such as a spin foam model. Very much in the spirit of condensedmatter models, fixed points of the Renormalization Group flow can provide a continuum limit in approaches such as Causal Dynamical Triangulations, spin foams, matrix and tensor models.
This workshop will for the first time bring together researchers working on different models of quantum gravity, who use the Renormalization Group in different forms. We will discuss conceptual as well as more technical questions, and establish a new dialogue between different quantum gravity approaches.
Sponsorship for this conference has been provided by:
Jan Ambjorn, Niels Bohr Institute
Benjamin Bahr, University of Hamburg
Dario Benedetti, Albert Einstein Institute
Alfio Bonanno, National Institute for Astrophysics
Sylvain Carozza, CPT Marseille
Joshua Cooperman, Radboud University Nijmegen
Bianca Dittrich, Perimeter Institute
John Donoghue, University of Massachusetts
Astrid Eichhorn, Perimeter Institute
ZhengCheng Gu, Perimeter Institute
Razvan Gurau, Université ParisSud XI Orsay
Petr Horava, Universityof California, Berkeley
Tim Koslowski, University of New Brunswick
Daniel Litim, University of Sussex
Renate Loll, Radboud University Nijmegen
Mercedes Martin Benito, Radboud University Nijmegen
Tim Morris, University of Southampton
Daniele Oriti, Albert Einstein Institute
Jan Pawlowski, University of Heidelberg
Martin Reuter, Johannes Gutenberg University
Vincent Rivasseau, Université ParisSud XI Orsay
James Ryan, Albert Einstein Institute
Dine Ousmane Samary, Perimeter Institute
Frank Saueressig, Radboud University Nijmegen
Lee Smolin, Perimeter Institute
Simone Speziale, CPT Marseille
Kellogg Stelle, Imperial College, London
 Jan Ambjorn, Niels Bohr Institute
 Benjamin Bahr, University of Hamburg
 Andrzej Banburski, Perimeter Institute
 Aristide Baratin, University of Waterloo
 Jacob Barnett, Perimeter Institute
 Dario Benedetti, Albert Einstein Institute
 Alfio Bonanno, National Institute for Astrophysics
 Sylvain Carozza, CPT Marseille
 Joshua Cooperman, Radboud University Nijmegen
 Bianca Dittrich, Perimeter Institute
 Pietro Dona, SISSA
 John Donoghue, University of Massachusetts
 Maite Dupuis, University of Waterloo
 Astrid Eichhorn, Perimeter Institute
 Laurent Freidel, Perimeter Institute
 Marc Geiller, Pennsylvania State University
 Florian Girelli, University of Waterloo
 Lisa Glaser, Niels Bohr Institute
 ZhengCheng Gu, Perimeter Institute
 Razvan Gurau, Université ParisSud XI Orsay
 Hal Haggard, Centre de Physique Theorique de Luminy
 Petr Horava, University of Clifornia, Berkeley
 Tim Koslowski, University of New Brunswick
 Stefan Lippoldt, University of Jena
 Daniel Litim, University of Sussex
 Renate Loll, Radboud University Nijmegen
 Mercedes Martin Benito, Radboud University Nijmegen
 Tim Morris, University of Southampton
 Daniele Oriti, Albert Einstein Institute
 Carlo Pagani, SISSA
 Jan Pawlowski, University of Heidelberg
 Roberto Percacci, SISSA
 Luis Pires, Radboud University Nijmegen
 Martin Reuter, Johannes Gutenberg University
 Aldo Riello, CPT Luminy, AixMarseille Universit
 Vincent Rivasseau, Université ParisSud XI Orsay
 James Ryan, Albert Einstein Institute
 Dine Ousmane Samary, Perimeter Institute
 Frank Saueressig, Radboud University Nijmegen
 Giuseppe Sellaroli, University of Waterloo
 Lee Smolin, Perimeter Institute
 Simone Speziale, CPT Marseille
 Sebastian Steinhaus, Perimeter Institute
 Kellogg Stelle, Imperial College, London
 Dejan Stojkovic, University of Buffalo
 Tomasz Trzesniewski, University of Wroclaw
 Gian Paolo Vacca, National Institute for Nuclear Physics
 Wolfgang Wieland, Pennsylvania State University
Renormalization Group Approaches to Quantum Gravtiy
Tuesday, April 22, 2014
Time 
Event 
Location 
8:30 – 9:00am 
Registration 
Reception 
9:00 – 9:10am 
Welcome and Opening Remarks 
Bob Room 
9:10 – 10:10am 
Overview Asymptotic Safety Tim Morris, University of Southampton 
Bob Room 
10:10 – 11:10am 
Overview Causal Dynamical Triangulations Renate Loll, Radboud University Nijmegen 
Bob Room 
11:10 – 11:40am 
Break 
Bistro – 1^{st} Floor 
11:40 – 11:50am 
Conference Photo 
Atrium 
11:50 – 12:40pm 
Overview Tensor Track Razvan Gurau, Université ParisSud XI Orsay 
Bob Room 
12:40 – 2:30pm 
Lunch 
Bistro – 2^{nd} Floor 
2:30 – 3:20pm 
Overview Renormalization in Group Field Theories Daniele Oriti, Albert Einstein Institute 
Bob Room 
3:20 – 4:20pm 
Overview Renormalization in Spin Foams Bianca Dittrich, Perimeter Institute 
Bob Room 
4:20 – 4:50pm 
Break 
Bistro – 1^{st} Floor 
4:50 – 6:00pm 
Challenge Talks Lee Smolin, Perimeter Institute & 
Bob Room 
Wednesday, April 23, 2014
Poster Session opens Wednesday morning
Time 
Event 
Location 
9:00 – 9:40am
9:40 – 10:20am 
Connecting the RG in gravity to phenomenology John Donoghue, University of Massachusetts Daniel Litim, University of Sussex 
Bob Room

10:20 – 11:00am 
Break 
Bistro – 1^{st} Floor 
11:00 – 11:40am 11:40 – 12:20pm 
Connecting the RG in gravity to phenomenology cont. Alfio Bonanno, INAF Kellogg Stelle, Imperial College, London 
Bob Room 
12:20 – 1:00pm 
Discussion of morning talks (How) can we extract phenomenological consequences of the RG flow in gravity? 
Bob Room 
1:00 – 2:00pm 
Lunch 
Bistro – 2^{nd} Floor 
2:00  3:30pm 
Perimeter Institute Colloquium 
Theater 
3:30 – 4:10pm 4:10 – 4:50pm 
Connections between methods and results from different approaches Tim Koslowski, University of New Brunswick Jan Ambjorn, Niels Bohr Institute 
Bob Room 
4:50  5:10pm  Break  Bistro – 1^{st} Floor 
5:10 – 5:50pm 
Connections between methods and results from different approaches cont. Mercedes MartinBenito, Radboud University Nijmegen 
Bob Room 
5:50 – 6:40pm 
Discussion Is there a relation between some approaches? 
Bob Room 
6:45pm 
Banquet 
Bistro – 2^{nd} Floor 
Thursday, April 24, 2014
Time 
Event 
Location 
9:00 – 9:40am
9:40 – 10:20am

Renormalization Group in gravity and symmetries ZhengCheng Gu, Perimeter Institute Jan Pawlowski, University of Heidelberg 
Bob Room 
10:20 – 11:00am 
Break 
Bistro – 1^{st} Floor 
11:00 – 11:40am 
Renormalization Group in gravity and symmetries cont. Benjamin Bahr, University of Hamburg 
Bob Room 
11:40 – 12:00pm 
Discussion What is the meaning of the Renormalization Group scale in a diffeomorphism invariant theory? 
Bob Room 
12:00 – 12:30pm 
Discussion What is the role of the Planck length in RG approaches 
Bob Room 
12:30 – 2:30pm 
Lunch 
Bistro – 2^{nd} Floor 
2:30 – 3:10pm
3:10 – 3:50pm 
Lorentz invariance and the RG flow in gravity Petr Horava, University of California, Berkeley Dario Beneditti, Albert Einstein Institute 
Bob Room

3:50 – 4:30pm 
Break 
Bistro – 1^{st} Floor 
4:30 – 5:10pm 
Lorentz invariance and the RG flow in gravity cont. Frank Saueressig, Radboud University Nijmegen 
Bob Room 
5:10 – 6:00pm 
Discussion What are the mechanisms for restoration of symmetry during 
Bob Room 
6:00pm 
Pub Night 
Bistro 
Friday, April 25, 2014
Time 
Event 
Location 
9:00 – 9:40am
9:40 – 10:20am 
What are the fundamental gravitational degrees of freedom? Martin Reuter, Johannes GutenbergUniversität Mainz Astrid Eichhorn, Perimeter Institute 
Bob Room 
10:20 – 11:00am 
Break 
Bistro – 1^{st} Floor 
11:00 – 11:40am 
What are the fundamental gravitational degrees of freedom?cont. Joshua Cooperman, Radboud University Nijmegen 
Bob Room 
11:40 – 12:20pm 
Discussion What are the degrees of freedom we should use in a gravitational path integral? 
Bob Room 
12:20 – 2:30pm 
Lunch 
Bistro – 2^{nd} Floor 
2:30 – 3:10pm 3:10 – 3:50pm 
Renormalization Group in spacetime vs. group space Sylvain Carrozza, CPT Marseille Vincent Rivasseau, Université ParisSud XI Orsay 
Bob Room 
3:50 – 4:30pm 
Break 
Bistro – 1^{st} Floor 
4:30 – 5:10pm 
Renormalization Group in spacetime vs. group space cont. James Ryan, Albert Einstein Institute 
Bob Room 
5:10 – 6:00pm 
Discussion What is the meaning of asymptotic freedom or asymptotic 
Bob Room 
6:30pm 
Casual Dinner – Details TBA 
Offsite 
Jan Ambjorn, Niels Bohr Institute
RG flow in CDT
An attempt is made to define "lines of contant physics" in CDT and relate the corresponding picture to nontrivial UV fixed points as they appear in the asymptotic safety scenario.
Benjamin Bahr, University of Hamburg
On backgroundindependent renormalization in statesum models
In this talk we discuss some notion of coarse graining in statesums, most notably a class of spin foam models in their holonomy representations. We discuss the notion of scale in this context, and how diffeomorphisminvariance ties into the existence of a continuum limit. We close with an example and muse about the interplay between diffeomorphisminvariance and nonrenormalizability.
Dario Benedetti, Albert Einstein Institute
Oneloop renormalization in a toy model of HoravaLifshitz gravity
I will present some recent results on the UV properties of a toy model of HoravaLifshitz gravity in 2+1 dimensions. In particular, I will illustrate some details of a oneloopcalculation, leading to beta functions for the running couplings. The renormalization group flow obtained in such way shows that Newton's constant is asymptotically free. However, the DeWitt supermetric approaches its Weyl invariant form with the same speed and the effective interaction coupling of the scalar degree of freedom remains constant along the flow. I will discuss some general lesson that we can learn from these results.
Alfio Bonanno, INAF
Confronting Asymptotically Safe Inflation with Planck data
Sylvain Carrozza, CPT Marseille
Renormalization group approach to 3d group field theory
I will start with a brief overview of tensorial group field theories with gauge invariant condition and their relation to spin foam models. The rest of the talk will be focused on the SU(2) theory in dimension 3, which is related to Euclidean 3d quantum gravity and has been proven renormalizable up to order 6 interactions. General renormalization group flow equations will be introduced, allowing in particular to understand the behavior of the relevant couplings in the neighborhood of the Gaussian fixed point. I will close with preliminary investigations about the existence of a nontrivial fixed point.
Joshua Cooperman, Radboud University Nijmegen
Renormalization of entanglement entropy and the gravitational effective action
The entanglement entropy associated with a spatial boundary in quantum field theory is ultraviolet divergent, its leading term being proportional to the area of the boundary. Callan and Wilczek proposed a geometrical prescription for computing this entanglement entropy as the response of the gravitational effective action to a conically singular metric perturbation. I argue that the CallanWilczek prescription is rigorously justified at least for a particular class of quantum states each expressible as a Euclidean path integral. I then show that the entanglement entropy is rendered ultraviolet finite by precisely the counterterms required to cancel the ultraviolet divergences in the gravitational effective action. In particular, the leading contribution to the entanglement entropy is given by the renormalized BekensteinHawking formula. These results apply to a general quantum field theory coupled to a fixed background metric, holding for arbitrary entangling surfaces with vanishing extrinsic curvature in any dimension, to all orders in perturbation theory in the quantum fields, and for all ultraviolet divergent terms in the entanglement entropy. I also reconcile these results on the entanglement entropy with the existing literature, compare them to the Wald entropy, and speculate on their interpretation and implication.
Bianca Dittrich, Perimeter Institute
Quantum Spacetime Engineering
John Donoghue, University of Massachusetts
Perturbative quantum gravity calculations and running couplings
We know how to make perturbative calculations in quantum gravity using the framework of effective field theory. I will describe the basics of the effective field theory treatment and look at several calculations. There are obstacles to describing these with running coupling constants. Finally, I will do my best to try to connect these with the Asymptotic Safety program.
Astrid Eichhorn, Perimeter Institute
Why matter matters in quantum gravity
I will argue that a fundamental theory of quantum gravity that is applicable to our universe must include matter degrees of freedom. In my talk I will focus on the option that these are fundamental, in contrast to lowenergy effective, degrees of freedom, and must thus be included in the microscopic dynamics of spacetime.
I will present evidence that dynamical Standard Model matter is compatible with asymptotically safe quantum gravity, while several "Beyond Standard Model" scenarios are disfavored. I will also discuss how the coupling to matter opens a window into the observational quantum gravity regime.
ZhengCheng Gu, Perimeter Institute
Grassmann tensor network renormalization and fermionic topological quantum field theory: a new route towards quantum gravity
Razvan Gurau, Université ParisSud XI Orsay
Tensor Models in the Large N limit
Tensor models generalize matrix models and provide a framework for the study of random geometries in arbitrary dimensions. Like matrix models they support a 1/N expansion, where N is the size of the tensor, with an analytically controlled large N limit. In this talk I will present some recent results in this field and I will discuss their implications for quantum gravity.
Petr Horava, University of California, Berkeley
Phases of Gravity
Quantum gravity with anisotropic scaling exhibits a rich structure of phases and phase transitions, dominated by multicritical behavior dependent on the spacetime dimension and the dynamical critical exponent. I will discuss some features of this phase structure, as well as its similarities and differences in comparison to the CDT approach to quantum gravity.
Tim Koslowski, University of New Brunswick
Asymptotic safety in a pure matrix model
The connection between twodimensional Euclidean gravity and pure matrix models has lead to may fundamental insights about quantum gravity and string theory. The pure matrix model is thus a blueprint for the connection between discrete models and Euclidean quantum gravity. I will report on work with Astrid Eichhorn in which this "blueprint" model is investigated with the functional renormalization group. In this model, I will discuss the questions: "What is a possible meaning of asymptotic safety in a discrete model?" and "Is it possible to apply the FRGE to tensor models?
Daniel Litim, University of Sussex
Lessons from asymptotic safety
Two aspects of asymptotic safety are highlighted. First, I discuss how asymptotic safety can be tested with the help of a bootstrap strategy. This is then applied to highorder polynomial actions of the Ricci scalar and beyond. Second, I discuss how phenomenological signatures of asymptotic safety can be searched for at particle colliders such as the LHC, provided that the quantum gravity scale is in the TeV energy regime.
Renate Loll, Radboud University Nijmegen
What you always wanted to know about CDT, but did not have time to read about in our papers
I will review the approach of Causal Dynamical Triangulations to nonperturbative quantum gravity, highlighting some frequently mis or ununderstood features, emphasizing recent developments and discussing some interesting open issues.
Mercedes MartinBenito, Radboud University Nijmegen
Refinement limit of quantum group spinnets
The manybuildingblocks limit of spin foam models remains to be an open question. The complexity of these models makes the analysis of their possible continuum phases a very difficult task. In the last years progress in this direction has been made by considering simplified, yet featuredrich, analog models to spin foams, the socalled spin net models. These models retain the main dynamical ingredient of spin foams, namely the simplicity constraints. In this talk we will introduce spin net models based on the quantum group SU(2)_q, and we will review the use of tensor network renormalization group techniques to study their coarse graining. We will analyze the resulting phase diagram, which interestingly displays a rich structure of fixed points. Furthermore we will discuss the relation of spin nets with spin foams.
Tim Morris, University of Southampton
Recent developments in asymptotic safety: tests and properties
The talk will review recent tests of the asymptotic safety conjecture within functional renormalisation group studies and progress in understanding the properties that such a fixed point would have.
Daniele Oriti, Albert Einstein Institute
Renormalization of group field theories: motivations and a brief review
Group field theories are tensorial models enriched with grouptheoretic data in order to define proper field theories of quantum geometry. They can be understood as a second quantised (Fock space) reformulation of loop quantum gravity kinematics and dynamics. The renormalization group provides, as a in any quantum field theory, a key tool to select welldefined models, to unravel the impact of quantum effects on the dynamics across different scales, and to study the continuum limit. Beside introducing the general formalism and clarifying the relation to other approaches, we will motivate the renormalisation group analysis of group field theories and review recent developments in this direction.
Jan Pawlowski, University of Heidelberg
Global flows in quantum gravity
In this talk I present recent work on complete UVIR flows for the fully momentumdependent propagator, RGconsistent vertices, Newtons coupling and the cosmological constant. For the first time, a global phase diagram is obtained where the nonGaussian ultraviolet fixed point of asymptotic safety is connected via smooth trajectories to an infrared fixed point with classical scaling. Physics implications as well as the extension to gaugemattergravity systems are discussed.
Martin Reuter, Johannes GutenbergUniversität Mainz
The Asymptotic Safety Program: new results and an inconvenient truth
We briefly review the various components and their conceptual status of the full Asymptotic Safety Program which aims at finding a nonperturbative infinitecutoff limit of a regularized functional integral for a quantum field theory of gravity. It is explained why in the continuum formulation based on the Effective Average Action the key requirement of background independence unavoidably results in a "bimetric" framework, and recent results on truncated RG flows of bimetric actions are presented. They suggest that the next generation of truncations that must be explored should be of bimetric type. As an application, a method of characterizing and counting physical states is shown to arise.
Vincent Rivasseau, Université ParisSud XI Orsay
Between Matrices and Tensors
Quartic tensor models can be rewritten in terms of intermediate matrix fields. The corresponding expansion is not only simpler, it suggests also new bridges between matrices, strings and tensors.
James Ryan, Albert Einstein Institute
Double scaling in tensor models
I present recent work on the double scaling limit of random tensor models through the analysis of their SchwingerDyson equations. This study exemplifies their potential for probing the continuum phase structure of these theories.
Frank Saueressig, Radboud University Nijmegen
Gravitational RG flows on foliated spacetimes
The role of time and a possible foliation structure of spacetime are longstanding questions which lately received a lot of renewed attention from the quantum gravity community. In this talk, I will review recent progress in formulating a Wetterichtype functional renormalization group equation on foliated spacetimes and outline its potential applications. In particular, I will discuss first results concerning the RG flow of HoravaLifshitz gravity, highlighting a possible mechanism for a dynamical Lorentzsymmetry restoration at low energies.
Kellogg Stelle, Imperial College, London
What happens to the Schrödinger solution in quantum corrected gravity?
Global flows in quantum gravity
In this talk I present recent work on complete UVIR flows for the fully momentumdependent propagator, RGconsistent vertices, Newtons coupling and the cosmological constant. For the first time, a global phase diagram is obtained where the nonGaussian ultraviolet fixed point of asymptotic safety is connected via smooth trajectories to an infrared fixed point with classical scaling. Physics implications as well as the extension to gaugemattergravity systems are discussed.
Grassmann tensor network renormalization and fermionic topological quantum field theory: a new route towards quantum gravity
Recently, the development of tensor network renormalization approach has provided us a powerful tool to construct new classes of topological quantum field theories(TQFTs) in discrete spacetime. For example, the Turaev Viro’s states sum constructions are fixed point tensor networks representing a special class of 2+1D TQFTs. Interestingly, the Grassmann variable generalization of tensor network renormalization approach leads to new classes of TQFTs for interacting fermion systems, namely, the fermionic TQFTs.
Refinement limit of quantum group spinnets
The manybuildingblocks limit of spin foam models remains to be an open question. The complexity of these models makes the analysis of their possible continuum phases a very difficult task. In the last years progress in this direction has been made by considering simplified, yet featuredrich, analog models to spin foams, the socalled spin net models. These models retain the main dynamical ingredient of spin foams, namely the simplicity constraints.
Asymptotic safety in a pure matrix model
An attempt is made to define "lines of contant physics" in CDT and relate the corresponding picture to nontrivial UV fixed points as they appear in the asymptotic safety scenario.
Asymptotic safety in a pure matrix model
The connection between twodimensional Euclidean gravity and pure matrix models has lead to may fundamental insights about quantum gravity and string theory. The pure matrix model is thus a blueprint for the connection between discrete models and Euclidean quantum gravity. I will report on work with Astrid Eichhorn in which this "blueprint" model is investigated with the functional renormalization group. In this model, I will discuss the questions: "What is a possible meaning of asymptotic safety in a discrete model?" and "Is it possible to apply the FRGE to tensor models?
What happens to the Schwarzschild solution in quantum corrected gravity?
Confronting Asymptotically Safe Inflation with Planck data
Lessons from asymptotic safety
Two aspects of asymptotic safety are highlighted. First, I discuss how asymptotic safety can be tested with the help of a bootstrap strategy. This is then applied to highorder polynomial actions of the Ricci scalar and beyond. Second, I discuss how phenomenological signatures of asymptotic safety can be searched for at particle colliders such as the LHC, provided that the quantum gravity scale is in the TeV energy regime.
Perturbative quantum gravity calculations and running couplings
We know how to make perturbative calculations in quantum gravity using the framework of effective field theory. I will describe the basics of the effective field theory treatment and look at several calculations. There are obstacles to describing these with running coupling constants. Finally, I will do my best to try to connect these with the Asymptotic Safety program.
What are the most pressing open questions in the application of the RG to gravity?
Pages
Scientific Organizers:
Bianca Dittrich, Perimeter Institute
Astrid Eichhorn, Perimeter Institute
Daniele Oriti, Albert Einstein Institute
Roberto Percacci, SISSA