Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

2019

J. High Energ. Phys.

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Constraining quantum gravity from observations is a challenge. We expand on the idea that the interplay of quantum gravity with matter could be key to meeting this challenge.Thus, we set out to confront different potential candidates for quantum gravity -unimodular asymptotic safety, Weyl-squared gravity and asymptotically safe gravity -with constraints arising from demanding an ultraviolet complete Standard Model. Specifically, we show that within approximations, demanding that quantum gravity solves the Landau-pole problems in Abelian gauge couplings and Yukawa couplings strongly constrains the viable gravitational parameter space. In the case of Weyl-squared gravity with a dimensionless gravitational coupling, we also investigate whether the gravitational contribution to beta functions in the matter sector calculated from functional Renormalization Group techniques is universal, by studying the dependence on the regulator, metric field parameterization and choice of gauge. I. INTRODUCTIONObservational constraints on quantum gravity are hard to come by. Based on a simple dimensional argument, one typically expects a power-law suppression of quantum-gravity effects 1 with (E/M Pl ) # , with E being the energy scale relevant for experiments, M Pl being the Planck mass and # > 0. Nevertheless, mathematical and internal consistency are not the only conditions that could * Electronic address: gpbrito@cbpf.br † Electronic address: eichhorn@sdu.dk ‡ Electronic address: adpjunior@id.uff.br 1 In the presence of a second "meso"-scale, as hinted at by some quantum-gravity approaches, e.g., [1], this situation can change.

Section: Introduction To (Unimodular) Asymptotically Safe Gravitymentioning

confidence: 99%

A link that matters: towards phenomenological tests of unimodular asymptotic safety

Brito

Eichhorn

2019

J. High Energ. Phys.

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“…Nevertheless, this opens an exciting possibility to explicitly compare critical exponents in more refined calculations and check whether this premature conclusion could be indeed realized. Results obtained in the simplest truncation for rank-4 models were also reported in [111].…”

Section: Background-independent Renormalization Group Flowsmentioning

confidence: 80%

Quantum Spacetime and the Renormalization Group: Progress and Visions

Progress and Visions in Quantum Theory in View of Gravity

2020

“…and T a1b1c1d1 T a2b2c2d1 T a2b2c2d2 · ·T a1b1c1d2 all come with the same coupling in this model, but nevertheless all have to be included in the effective dynamics. In [59] index permutation was treated anisotropically. In many cases, color-anisotropic fixed points feature an enhanced symmetry which implies the reduction of the effective dynamics to lower-rank tensor models [56], motivating us to explore the model with isotropy under index permuations.…”

Section: The Modelmentioning

confidence: 99%

Universal critical behavior in tensor models for four-dimensional quantum gravity

Eichhorn

Lumma

et al. 2020

J. High Energ. Phys.

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Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a model by employing background-independent coarse-graining techniques where the tensor size serves as a pre-geometric notion of scale. A fixed point candidate which features two relevant directions is found. The possible relevance of this result in view of universal results for quantum gravity and a potential connection to the asymptotic-safety program is discussed. I. THE CASE FOR UNIVERSAL, BACKGROUND-INDEPENDENT QUANTUM GRAVITYTo describe physically relevant spacetimes, such as black holes or Friedmann-Lemaitre-Robertson-Walker spacetimes, it is necessary to go beyond General Relativity, where these spacetimes feature singularities. Such singularities are expected to be resolved once quantum fluctuations of spacetime are properly accounted for. Yet, this is a particularly challenging task if it is to be compatible with the background-independence at the heart of our modern understanding of gravity. Backgroundindependence implies that no configuration of spacetime should be singled out a priori from all configurations that enter the path integral. This is incompatible with perturbative techniques around a fixed spacetime, which single out a special background to perturb around, and which do not provide a predictive quantum field theory of gravity. Instead, one is led to introduce an infinite number of independent local counterterms to cancel divergences at each loop order [1][2][3]. This motivates that background independence should be taken seriously in the search for an ultraviolet complete definition of the gravitational path integral. Thus, we aim at an implementation of the path integral without auxiliary geometric background structures 1 . A promising route to construct a background independent path integral consists of making a transition to discrete building blocks, as in dynamical triangulations [5], Regge calculus [6], matrix/tensor models [7-9], spin foams [10] and causal sets [11]. This allows to construct a discrete approximation of all random geometries (and potentially additional configurations with no interpreta- * eichhorn@cp3.sdu.dk † j.lumma@thphys.uni-heidelberg.de ‡ adpjunior@id.uff.br § a.sikandar@thphys.uni-heidelberg.de 1 An alternative route makes use of an auxiliary background structure at the technical level while ensuring the independence of physical results from this background structure, see, e.g., [4].tion as a spacetime geometry) that enter the path integral for quantum gravity. These discrete building blocks are typically not viewed as physical, "fundamental" building blocks of spacetime. Rather, they are auxiliary, unphysical entities, allowing to define a regularized path integral in analogy to lattice gauge theories for non-gravitational quantum field theories. One might object that quantum spacetime might be fundamentally discrete, wh...