Probing the Fundamental Nature of Spacetime with the Renormalization Group

Mar 23, 2015, 9:00 AM → Mar 27, 2015, 6:00 PM Europe/Stockholm

132:028 (Nordita, Stockholm)

Astrid Eichhorn (Perimeter Institute), Dario Benedetti (Albert-Einstein-Institute, Golm), Frank Saueressig (Radboud University Nijmegen)

Venue

Nordita, Stockholm, Sweden

Scope

Renormalization group methods are a key element of theoretical particle physics and may also be central for constructing a fundamental theory of gravity, e.g., based on Weinberg’s asymptotic safety conjecture. The aim of this program is to bring together theorists and phenomenologists in order to discuss ideas related to the application of the renormalization group in quantum gravity and the consequences of asymptotic safety for cosmology, black holes and a possible ultraviolet completion of the standard model of particle physics including gravity.

[Timetable - available from start of the program]

Format

This meeting will focus on three broadly defined topics: Structural aspects of asymptotic safety, phenomenological implications of asymptotic safety in gravity and particle physics, and relations of asymptotically safe quantum gravity to other approaches to quantum gravity. Each topic will be addressed by several talks outlining the present status of the research program and possibly opening up new perspectives. The schedule will contain ample room for discussion and collaboration.

There will be approximately five talks per day, with the exception of Wednesday afternoon, which is reserved for in-depth discussion.

Invited Speakers

Alfio Bonanno, INFN Sezione di Catania Alessandro Codello, CP3-Origins & Danish IAS University of Southern Denmark Joshua Cooperman, Radboud University Nijmegen Bianca Dittrich, Perimeter Institute, Waterloo Holger Gies, Friedrich-Schiller University Jena Andrzej Görlich, Niels Bohr Institute Copenhagen & Jagellonian University Krakow Razvan Gurau, Ecole Polytechnique Daniel Litim, University of Sussex Renate Loll, Radboud University Nijmegen

Tim Morris, University of Southampton Jan Pawlowski, University of Heidelberg Roberto Percacci, INFN Sezione di Trieste & SISSA Martin Reuter, Johannes-Gutenberg University Mainz Vincent Rivasseau, Universite Paris XI Orsay Francesco Sannino, CP3-Origins & Danish IAS University of Southern Denmark Omar Zanusso, Radboud University Nijmegen

Application

If you want to apply for participation in the workshop, please fill in the application form. You will be informed by the organizers shortly after the application deadline whether your application has been approved. Due to space restrictions, the total number of participants is strictly limited. (Invited speakers are of course automatically approved, but need to register anyway.)

Application deadline: 10 October 2014

There is no registration fee.

Travel Reimbursement

PhD students and young Postdoc fellows are eligible for travel grants to participate in the program. If you are interested in such a grant, please mark the corresponding field in the application form, briefly summarize your interest in the program in the comments field, and indicate an estimation of your expected travel expenses. Since only a limited number of grants is available, decision concerning the grants will be made on a case-by-case basis and you will be notified shortly after the application deadline.

Accommodation

Nordita provides a limited number of rooms in the Stockholm apartment hotel BizApartments free of charge for accepted participants.

Sponsored by:

Monday, March 23

9:00 AM → 9:10 AM Registration - Welcome

9:10 AM → 10:40 AM Asymptotic Safety in the bi-metric era

After a brief review of the main structural properties of the bi-metric implementation of Background Independence, some recent results obtained by means of bi-metric truncations of the effective average action will be discussed. The focus of the talk is on the possible existence of a "C-theorem" in 4 dimensional QEG, some of the pressing positivity issues in QEG, and, more technically, on new reliability tests for truncations which can be applied to any theory.

Speaker: Martin Reuter

Slides 2015-03-23-reuter.pdf

10:40 AM → 11:10 AM break

11:10 AM → 12:00 PM Background independent exact renormalization group for conformally reduced gravity

Within the conformally reduced gravity model, where the metric is parametrised by a function of the conformal factor field, we keep dependence on both the background and fluctuation fields, to local potential approximation and order derivative-squared respectively, making no other approximation. The functional dependence on the background field is then dictated by realising a remnant diffeomorphism invariance. The standard non-perturbative Renormalization Group (RG) scale is inherently background dependent, which we show in general forbids the existence of RG fixed points. By combining the flow equations with the modified split Ward identity, we uncover a unique background independent notion of RG scale. The corresponding RG flow equations are then not only explicitly background independent along the entire RG flow but also explicitly independent of the way the conformal factor is parametrised.

Speaker: Tim Morris

Slides 2015-03-23-morris.pdf

12:00 PM → 2:10 PM lunch

2:10 PM → 3:00 PM Fluctuations, locality and the phase structure of quantum gravity

In this talk I present results for UV-IR flows for fully momentum-dependent propagators, vertices in quantum gravity.  The momentum locality of the underlying block-spinning procedure is related to diffeomorphism invariance. The setting is used to compute  the scale-dependent Newton coupling and the cosmological constant. Physics implications as well as the extension to gauge-matter-gravity systems are discussed.

Speaker: Jan Pawlowski

Slides 2015-03-23-pawlowski.pdf

3:00 PM → 3:30 PM break

3:30 PM → 4:20 PM One-loop beta-function for an infinite-parameter family of gauge theories

Any field theory is renormalisable once all terms compatible with the symmetries are added to the Lagrangian. One can then in principle attempt to compute the arising renormalisation group flow, and search for fixed points realising the asymptotic safety scenario. However, in practice the terms one needs to add to the Lagrangian contain higher derivatives, and the necessary computation, even at one loop, becomes unrealistic. I report on a one-loop computation where the salting point is taken to be the family of Lagrangians given by an arbitrary function of the self-dual part of the Yang-Mills curvature tensor. All such Lagrangians lead to just second order in derivatives field equations, and so seem to be clearly insufficient to renormalise the arising divergences. However, as I will show, the magic of self-duality makes this family of theories one-loop renormalisable. I will explicitly describe the arising renormalisation group flow in the infinite-dimensional space of coupling constants.

Speaker: Kirill Krasnov

Slides 2015-03-23-krasnov.pdf

4:20 PM → 5:10 PM Discussion

Tuesday, March 24

9:00 AM → 9:50 AM Wilson Loops in Causal Dynamical Triangulations

Speaker: Renate Loll

9:50 AM → 10:40 AM What is the large-scale effective action of (2+1)-dimensional causal dynamical triangulations?

The literature contains several analyses suggesting that the large-scale effective action of (2+1)-dimensional causal dynamical triangulations has the form of a minisuperspace model of projectable Horava-Lifshitz gravity. I weigh in on these suggestions by reporting the results of a comprehensive statistical analysis comparing several candidate effective actions.  Controversial Statement: The large-scale effective action of (3+1)-dimensional causal dynamical triangulations has the form of a minisuperspace model of Einstein gravity.

Speaker: Joshua Cooperman

Slides Cooperman_-_Nordita2015.pdf

10:40 AM → 11:10 AM break

11:10 AM → 12:00 PM RG flow in Causal Dynamical Triangulations

Causal Dynamical Triangulations (CDT) is a background independent approach to quantum gravity. In this talk I will present recent studies of the effective transfer matrix. The introduced method allows observing a possibly new 'bifurcation' phase. I will also define a notion of 'lines of constant physics’ in the coupling constant space and investigate the renormalization group flow in CDT.

Speaker: Andrzej Görlich

Slides 2015-03-24-goerlich.pdf

12:00 PM → 2:10 PM lunch

2:10 PM → 2:35 PM Real time renormalization

We present the real time formalism of the functional renormalization group method for the 3-dimensional $\phi^4$ theory. The original, single time formalism of the renormalization is based on the invariance of the transition amplitudes. By using the so-called closed time path formalism we will deduce the real time RG equations based on the invariance of the physically more relevant expectation values. In the case of zero temperature the phase space does not change qualitatively when we compare it by the ones obtained by the original RG treatment. The real time formalism enables us to take into account the finite temperature version of the $\phi^4$ theory in a simple manner. The evolution of the mixing couplings can account for the decoherence in the model.

Speaker: Sandor Nagy

Slides 2015-03-24-nagy.pdf

2:35 PM → 3:00 PM Asymptotic safety and scalar-tensor theories

I will focus on a class of scalar O(N) models non minimally coupled to gravity and discuss some results obtained within the functional renormalization group framework in the single metric truncation, using the exponential parametrization of the metric and a specific gauge fixing.

Speaker: Gian Paolo Vacca

Slides 2015-03-24-vacca.pdf

3:00 PM → 3:30 PM break

3:30 PM → 3:55 PM Scaling and Renormalization in Quantum Gravity

I will discuss scaling arguments in quantum gravity, in a covariant framework. After showing how these can be used to derive known results, such as the KPZ relations in the two dimensional case, I will describe how the renormalization group can be used together with scaling arguments to gain a deeper understanding of the theory at criticality.

Speaker: Giulio D'Odorico

3:55 PM → 4:20 PM Diffeomorphism invariance and critical scaling in quantum gravity

The problem of obtaining a gauge independent beta function for Newton's constant is addressed. By a specific parameterisation of metric fluctuations a gauge independent functional integral is constructed for the semiclassical theory around an arbitrary Einstein space. The effective action then has the property that only physical polarisations of the graviton contribute, while all other modes cancel with the functional measure. We are then able to compute a gauge independent beta function for Newton's constant in d-dimensions to one-loop order. Going beyond the semiclassical theory, by means of the exact renormalisation group, the beta function for Newton's constant is found within a simple approximation exploiting the gauge independent parameterisation. We then assess the scaling at an asymptotically safe fixed point. Close to two dimensions the critical exponent for Newton’s constant is found to be regulator independent. In four dimensions we apply Litim’s optimisation criteria on the space of regulators. The critical exponents is then found to agree with the value found in numerical lattice simulations by Hamber.

Speaker: Kevin Falls

Slides 2015-03-24-falls.pdf

4:20 PM → 5:10 PM Discussion

Wednesday, March 25

9:00 AM → 9:50 AM Asymptotic safety in perturbation theory and beyond

Speaker: Daniel Litim

Slides Litim_-_Nordita2015.pdf

9:50 AM → 10:40 AM Rethinking Naturalness: The Interacting Ultraviolet Safe Behaviour of Non-Abelian Gauge-Yukawa Theories

I will critically introduce, classify and discuss the fundamental open issues related to either composite or elementary extensions of the standard model.  As for the progress I will exhibit, among other things, the first proof of existence of nonsupersymmetric and non-asymptotically free 4D Gauge-Yukawa theories (structurally similar to the standard model) which are UV finite thanks to the existence of an exact interacting quantum UV fixed point in the gauge, Yukawa and scalar self-couplings. The quantum moduli space of the theory will also be precisely determined. Theories with this behaviour have been searched for on the lattice for the past several decades. Our results show the critical ingredients that are needed to construct these new classes of theories and offer a strategy for future lattice studies. I will then comment on the wide phenomenological impact of this discovery.

Speaker: Francesco Sannino

10:40 AM → 11:10 AM break

11:10 AM → 12:00 PM Search of scaling solutions in scalar-tensor gravity

We write new functional renormalization group equations for a scalar nonminimally coupled to gravity. Thanks to the choice of the parametrization and of the gauge fixing they are simpler than older equations and avoid some of the difficulties that were previously present. In three dimensions these equations admit, at least for sufficiently small fields, a solution that may be interpreted as a gravitationally dressed Wilson-Fisher fixed point. We also find for any dimension d>2 two analytic scaling solutions which we study for d=3 and d=4. One of them corresponds to the fixed point of the Einstein-Hilbert truncation, the others involve a nonvanishing minimal coupling.

Speaker: Roberto Percacci

12:00 PM → 2:10 PM lunch

2:10 PM → 7:10 PM free afternoon

Thursday, March 26

9:00 AM → 9:50 AM Constraining Asymptotically Safe Inflation with cosmological observations

Speaker: Alfio Bonanno

9:50 AM → 10:40 AM Effective Field Theory of Gravity and Cosmology

Speaker: Alessandro Codello

Slides Codello_-_Nordita2015.pdf

10:40 AM → 11:10 AM break

11:10 AM → 12:00 PM Ghost free and singularity free construction of gravity : classical and quantum aspects

I will discuss generalisation of Einstein's gravity in the ultraviolet by extending it to infinite derivative theory of gravity which can ameliorate cosmological and black hole singularities. Furthermore at quantum level such class of action can also be made finite up to 2 loops. Beyond 2 loops there are some conjectures.

Speaker: Anupam Mazumdar

Slides 2015-03-26-mazumdar.pdf

12:00 PM → 2:10 PM lunch

2:10 PM → 3:00 PM Probing the fundamental nature of fluctuating membranes with the Renormalization Group

Membranes provide exciting physical systems with a strong interplay between local order and geometric fluctuations. They are also a non-trivial arena, both theoretical and experimental, in which the findings of the non-perturbative renormalization group can be tested, thus enhancing the confidence of the same applications to quantum gravity. We will review the distinct universality classes of membranes, the corresponding order parameters and the effective long-range interactions, that determine the rich membranes' phase diagram. Guided by these results, we will attempt to draw some lesson that can be applied in the context of quantum gravity.

Speaker: Omar Zanusso

Slides 2015-03-27-zanusso.pdf

3:00 PM → 3:30 PM break

3:30 PM → 4:20 PM Phase transitions in Tensor Models

In tensor and matrix models, phase transitions are understood as a tuning to criticality of some parameters. But in field theory phase transitions are usually understood in terms of symmetry breaking and translations of the fields to non trivial vacua. In this talk I will discuss the relation between the two points of view.

Speaker: Razvan Gurau

Slides 2015-03-26-gurau.pdf

4:20 PM → 5:10 PM Tensor Models, from branched polymers to Brownian spheres

Ordinary tensor models of rank D ≥ 3 are dominated at large N by tree-like graphs, known as melonic triangulations. We shall show that non-melonic contributions can be enhanced consistently, leading to different types of large N limits. For instance the most generic quartic tensor model at rank 4, with maximally enhanced non-melonic interactions, displays a branched polymer phase and a 2D quantum gravity phase, and a transition between them whose entropy exponent is positive. This work is in collaboration with V. Bonzom and T. Delepouve.

Speaker: Vincent Rivasseau

Slides 2015-03-26-rivasseau.pdf

Friday, March 27

9:00 AM → 9:50 AM What defines and how to construct a theory of quantum gravity?

Motivated by the loop quantum gravity framework I discuss what requirements a theory of quantum gravity needs to satisfy and how one could possible construct such a theory. I will then consider  how these ideas apply to other frameworks.

Speaker: Bianca Dittrich

9:50 AM → 10:20 AM break

10:20 AM → 11:10 AM Fermions, gravity and chiral symmetry

Any quantum degree of freedom that has a simple overlap
with
an elementary
degree of freedom has the chance to probe the nature of
spacetime at the
fundamental level - simply by means of its inherent quantum
fluctuations.
Chiral fermions are a good candidate for such degrees of
freedom. Chiral
symmetry is in fact a sensitive probe for interactions on
all scales: chiral
symmetry breaking can be triggered by comparatively weak
interactions as well
as by specific large-scale structures. The fact that chiral
fermions can be
observed in nature hence also represents a probe of
spacetime properties. In
this talk, the various connections between fermions, gravity
and chiral
symmetry will be discussed, highlighting potential
implications for theories
of quantum gravity.

Speaker: Holger Gies

Slides 2015-03-27-gies.pdf

11:10 AM → 12:00 PM Discussion

12:00 PM → 2:00 PM lunch