Quantum Fields – from Fundamental Concepts to Phenomenological Questions

26 Sept 2018, 09:00 → 28 Sept 2018, 18:00 Europe/Berlin

02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

Understanding the structure of quantum field theories and their observational consequences beyond the realm of perturbation theory constitutes one of the central challenges in theoretical physics. Progress along this research frontier may be the key for answering fundamental questions related to the structure of space, time, and matter. Following the idea of “renormalizing the non-renormalizable”, this route may even allow for a unified description of all fundamental forces, including gravity, within the framework of renormalizable quantum field theories.

A central tool for exploring this essentially uncharted territory are functional methods based, e.g., on path integrals or functional renormalization group equations. This workshop will survey recent developments, flourishing from seminal contributions by Martin Reuter, and future opportunities in this field. The scientific focus will cover fundamental aspects and a discussion of possible quantum gravity signatures observable in particle physics, black holes, and cosmology. The goal is to develop new roadmaps for obtaining a description of our world valid on all scales and identify new connections between the fundamental descriptions and phenomenological consequences within the various approaches.

Invited Speakers:

Abhay Ashtekar	Ennio Gozzi
Daniel Becker	Renate Loll
Dario Benedetti	Max Niedermaier
Alfio Bonanno	Carlo Pagani
Steve Carlip	Alessia Platania
Alessandro Codello	Hartmann Römer
Bianca Dittrich	Christof Wetterich
Walter Dittrich	Andreas Wipf
Gerald Dunne

Proceedings of the workshop will be published by universe.

Executive Summary (PDF) Reuter13.pdf

Participants (PDF) IndicoParticipantslist_QFT2018.pdf

Wednesday 26 September

Welcome

Convener: Prof. Matthias Neubert (Johannes Gutenberg University Mainz)

Mathematical Physics

1 Riemann's Zeta Function in Mathematics and Physics

TBA

Speaker: Prof. Walter Dittrich

10:30 Coffee

Characterizing Quantum Spacetime

2 Anti-Newtonian Expansions and the Functional Renormalization Group

In QFT an Anti-Newtonian expansion perturbs around decoupled copies of a self-interacting quantum mechanical system, with subsequent coupling induced by spatial hopping terms. Such an expansion is developed for the effective action of 1+d dimensional scalar QFTs. A Functional Renormalization Group in the hopping parameter leads to a recursion for which an exact solution in terms of combinatorial graph rules is presented. Upon coupling to gravity a coordinated gravitational expansion is needed to account for the classical backreaction of scalar field inhomogeneities. In Einstein gravity, the Anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of dofs. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton's constant that maps the ADM action into its Anti-Newtonian limit. Its inverse restores dynamical spatial gradients and provides classically the coordinated gravitational expansion. We outline the prospects of an associated trivializing flow in the quantum theory.

Speaker: Dr Max Niedermaier (Department of Physics and Astronomy, University of Pittsburgh)

3 The problem of vacuum in quantum gravity: a view from Asymptotic Safety

We use the non-Gaussian fixed points (NGFPs) appearing in the renormalization group flow of gravity and gravity-matter systems to construct models of NGFP-driven inflation via a renormalization group improvement scheme. The cosmological predictions of these models depend sensitively on the characteristic properties of the NGFPs, including their position and stability coefficients, which in turn are determined by the field content of the underlying matter sector. We show that the NGFPs appearing in gravity-matter systems where the matter content is close to the one of the standard model of particle physics are compatible with cosmological data. Somewhat counterintuitively, the negative fixed point value of the dimensionless cosmological constant is essential for these findings.

Speaker: Dr Alfio Maurizio Bonanno (INAF Catania - INFN)

12:30 Lunch

Highlight Lecture: Dimension and Dimensional Reduction in Quantum Gravity

4 Dimension and Dimensional Reduction in Quantum Gravity

If gravity is asymptotically safe, we expect operators to exhibit anomalous scaling at the UV fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short distance dimensional reduction. I will review the evidence for this behavior — emphasizing the physical question of what one means by "dimension" in a quantum spacetime — and will discuss possible mechanisms that could explain the universality of this phenomenon.

Speaker: Prof. Steven Carlip (University of California at Davis)

14:30 Coffee

Structural Aspects of Quantum Field Theory

5 Universality in the epsilon-expansion

After reviewing the Functional reformulation of the standard Perturbative RG (FPRG), I'll describe the classification of universality classes in arbitrary dimension within the epsilon-expansion and the relative determination of CFT data. In the single component case, universality classes are represented by renormalizable scalar QFTs with self-interacting potentials of highest monomial φ^m below their upper critical dimensions dc = 2m/(m -2). For even integers, m ≥ 4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d = 2, while for odd m the theories are non-unitary and start at m = 3 with the Lee-Yang universality class. An important outcome of this analysis is the realization of the existence of a new non-trivial family of d = 3 universality classes with upper critical dimension dc = 10/3. Subsequently, I will show how the FPRG formalism allows a straightforward generalization to the multicomponent case, with almost no need for additional computations. The classification of multicomponent universality classes if far from complete and I will discuss the present state of knowledge with few examples, including Potts and O(N) models. I will conclude with a review and outlook of the application of the epsilon-expansion to Quantum Gravity.

Speaker: Dr Alessandro Codello

6 Multi-critical multi-field models: a CFT approach in leading order.

I present general results for the multi-critical multi-field models in d>2 recently obtained using CFT+Schwinger-Dyson methods without assuming any symmetry. Results in the leading non trivial order are derived consistently for several conformal data in full agreement with functional perturbative RG methods. I also discuss the special cases of Potts models with S_q symmetry having critical dimension d_c>3.

Speaker: Dr Gian Paolo Vacca (INFN)

Discussion of the day

Thursday 27 September

Characterizing Quantum Spacetime

7 Quantum gravity and the search for observables

Speaker: Prof. Renate Loll

8 Geometric operators in Asymptotic Safety

We consider the scaling properties of geometric operators such as parametrized curves, surfaces, and volumes in the context of the Asymptotic Safety scenario for Quantum Gravity. We also discuss the scaling properties of geodesics and their possible role in the Asymptotic Safety scenario.

Speaker: Dr Carlo Pagani

10:30 Coffee

Characterizing Quantum Spacetime

9 Is Lorentz symmetry relevant?

Among the several approaches to quantise gravity, one particular is Horava-Lifshitz gravity, claiming that Lorentz symmetry is broken microscopically, which might allow a perturbative renormalisation of gravity. For this scenario to be related to the real world, Lorentz symmetry must be restored on large scales to be consistent with countless experiments. I propose a new foliated renormalisation group equation which preserves background diffeomorphism symmetry if the initial action is invariant. With this, it can be investigated whether quantum effects enhance or diminish Lorentz symmetry violations.

Speaker: Dr Benjamin Knorr (Radboud University)

10 Towards a predictive ultraviolet completion for quantum gravity and the Standard Model

I will discuss recent progress towards an ultraviolet completion of the Standard Model induced by asymptotically safe quantum fluctuations of gravity. In particular, I will focus on a scenario to retrodict the top and bottom mass and the Abelian gauge coupling from asymptotic safety. In an approximation, antiscreening quantum-gravity fluctuations induce an asymptotically safe fixed point for the Abelian hypercharge leading to a uniquely fixed infrared value that is observationally viable for a particular choice of microscopic gravitational parameters. The unequal quantum numbers of the top and bottom quark lead to different fixed-point values for the top and bottom Yukawa under the impact of gauge and gravity fluctuations. This results in a dynamically generated mass difference between the two quarks. To work quantitatively, the preferred ratio of electric charges of bottom and top in our approximation lies in close vicinity to the Standard-Model value of Q_b/Q_t =-1/2.

Speaker: Dr Astrid Eichhorn

12:30 Lunch

Highlight Lecture: Quantum Gravity in the Sky?

11 Quantum Gravity in the sky?

Thanks to the spectacular observational advances since the 1990s, a `standard model' of the early universe has now emerged. However, since it is based on quantum field theory in curved space-times, it is not applicable in the Planck regime. Using techniques from loop quantum gravity, the theory can be extended over the 12 orders of magnitude in density and curvature from the onset of inflation all the way back to the Planck regime, providing us with a possible completion of the standard model. Contrary to a common belief, the resulting pre-inflationary dynamics can have observational consequences. Thus, there is now an an interesting interplay between fundamental theory and observations. The talk will provide a broad overview of these results.

Speaker: Prof. Abhay Ashtekar (Penn State)

14:30 Coffee

Young Speakers

12 Cosmological bounds on the field content of asymptotically safe gravity-matter models

We use the non-Gaussian fixed points (NGFPs) appearing in the renormalization group flow of gravity and gravity-matter systems to construct models of NGFP-driven inflation via a renormalization group improvement scheme. The cosmological predictions of these models depend sensitively on the characteristic properties of the NGFPs, including their position and stability coefficients, which in turn are determined by the field content of the underlying matter sector. We show that the NGFPs appearing in gravity-matter systems where the matter content is close to the one of the standard model of particle physics are compatible with cosmological data. Somewhat counterintuitively, the negative fixed point value of the dimensionless cosmological constant is essential for these findings.

Speaker: Ms Alessia Platania (Heidelberg University (ITP))

13 Asymptotic Safety, Background Independence and Unitarity

What should a fundamental theory of quantum gravity look like? While the theories united in the Standard Model of particle physics fulfill a standard set of requirements, gravity is special in the sense that spacetime itself becomes dynamical. The independence of any preset background geometry is thus at the root of every quantum generalization of general relativity, as is (nonperturbative) renormalizability. The latter started the long ongoing discussion on a suitable approach to quantum gravity, for it was shown, that standard "quantization" of the classical Einstein-Hilbert action led is not renormalizable. Higher derivatives might be the cure, however unitarity seems to be lost. In this talk, the aspects of background independence and unitarity are investigated within the Asymptotic Safety program to quantum gravity. While technically challenging, the studied cases indicated that instead of being a burden, both concepts might help as "standard candles" in the sky of all possible theories.

Speaker: Daniel Becker (Gymnasium Herkenrath)

Discussion of the day

18:00 Workshop Dinner

Held at the Proviantmagazin

Friday 28 September

Structural aspects of quantum spacetime

14 The large-N limit in tensor-valued field theories

The large-N limit of quantum field theories with fields in the fundamental or adjoint representation of a compact Lie group, such as O(N) or U(N), has been extensively studied over the years as a tool for accessing non-perturbative physics by analytic means. Not much has been done instead until recent years for the large-N limit of theories in tensor product representations, or in the fundamental representations of product groups, such as O(N)xO(N)xO(N). The situation has recently changed thanks to two developments: the discovery that the large-N limit of such theories selects melonic Feynman diagrams, and the realization that such limit can lead to new interesting models of AdS/CFT correspondence. In this talk, I will briefly review such developments and I will present some new results about a tensor generalization of the Gross-Neveu model.

Speaker: Dr Dario Benedetti

15 Vacuum effective actions and the decoupling limit of quantum gravity

We discuss the low-energy gravitational effective action induced by quantum fluctuations of two- and four-dimensional massive matter fields. We show that the effective action agrees with expectations based on the Appelquist-Carazzone theorem and provide a renormalization group interpretation of the results which is rather scheme-independent in that it does not depend explicitly on a cutoff scale. Our findings point at interesting but still unexplored properties of the beta function of the Newton's constant and its bottom-up relation with conformal field theory.

Speaker: Dr Omar Zanusso

10:30 Coffee

Structural aspects of quantum spacetime

16 Quantum gravity from the boundary: holography and renormalization

A quantum gravity theory should yield a prescription of how to assign quantum amplitudes to arbitrary boundary geometries. I will describe a renormalization program for background independent theories, where the coarseness of the boundary data is used to define a notion of scale and truncations for the renormalization flow. This allows to bootstrap the amplitudes from coarse to finer and finer amplitudes. I will then explore holographic properties of quantum gravity amplitudes for general, not necessarily asymptotic boundaries. We will see that three-dimensional quantum gravity allows for a holographic dual description, with a dual local field describing the embedding of the boundary into the higher dimensional space time. In the four-dimensional case a similar descriptions holds for the flat sector of the theory. Including curvature degrees of freedom leads to non-localities in the dual field.

Speaker: Prof. Bianca Dittrich

17 Wicked Metrics

I will discuss various definitions of Wick rotation in a gravitational context and argue in favor of a definition where it is viewed as an analytic continuation of the metric. I will then show that also this definition has severe shortcomings. In particular, it may not always be possible to preserve the field Equations and the symmetries at global level.

Speaker: Prof. Roberto Percacci

12:30 Lunch

Highlight Lecture: Resurgence and Non-perturbative Physics

18 Resurgence and Non-perturbative Physics

Resurgence is a new approach to quantum field theory that combines perturbative and non-perturbative effects in a unified framework. The primary motivation is to uncover new computationally practical methods for path integrals in strongly interacting finite density and non-equilibrium systems. I'll give an overview of the key ideas and discuss applications to quantum field theory, matrix models and quantum mechanics, where new relations between perturbative and non-perturbative sectors have been discovered.

Speaker: Prof. Gerald Dunne (University of Connecticut)

14:30 Coffee

Effective field theory for gravity

19 Infrared quantum gravity: Status report

Although perturbatively non-renormalizable, general relativity is a perfectly valid quantum theory at low energies. Treated as an effective field theory one is able to make genuine quantum predictions by applying the conventional rules of quantum field theory. The low energy degrees of freedom and couplings of quantum gravity are fully dictated by the symmetries of general relativity. At long distances, the leading quantum corrections are precisely induced by the low-energy fluctuations of the massless graviton. Non-local effective actions efficiently encode the latter class of quantum corrections. In this talk I will provide an overview of recent progress in infrared quantum gravity.

Speaker: Dr BASEM ELMENOUFI (UNIVERSITY OF SUSSEX)

20 Towards the quantum effective action(s) of gravity

By definition, the quantum effective action describes the dynamics of a theory taking all quantum effects into account. Conceptually, it may provide an important bridge between the fundamental description of gravity and its phenomenological consequences. This talk outlines a new approach to construct the quantum effective action for gravity based on correlation functions. This approach gives access to both the local and non-local interactions appearing in the effective description. As a first application we discuss the partial reconstruction of the quantum effective action from correlation functions obtained within the Causal Dynamical Triangulations program.

Speaker: Dr Frank Saueressig (Radboud University Nijmegen)

Discussion of the day