Towards phase transitions between discrete and continuum quantum spacetime from the renormalization group

Eichhorn, Astrid; Koslowski, Tim

doi:10.1103/physrevd.90.104039

Cited by 49 publications

(71 citation statements)

References 110 publications

(133 reference statements)

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“…It represents a good opportunity for further applications of the FRG to GFTs, which would be undeniably valuable if they were available in 4d quantum gravity models. The FRG has recently been applied to matrix models and TGFTs without gauge invariance condition [33,49,50], hence we think that the D = 3 model of the present paper is the natural next step in this research direction, and it could provide a UV completion of otherwise diverging renormalization group trajectories. We also proposed a speculative idea towards a more physical application, would the existence of this fixed point be confirmed: its presence might favor dynamically generated ultra-local theories in the infrared, hence possibly evading the question of the gravitational interpretation of the bare Laplace-type propagator.…”

Section: Discussionmentioning

confidence: 99%

Group field theory in dimension4−ϵ

Carrozza

2015

Phys. Rev. D

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Building on an analogy with ordinary scalar field theories, an ε-expansion for rank-3 tensorial group field theories with gauge invariance condition is introduced. This allows to continuously interpolate between the dimension four group SU(2) × U(1) and the dimension three SU(2). In the first situation, there is a unique marginal ϕ 4 coupling constant, but in contrast to ordinary scalar field theory this model is asymptotically free. In the SU(2) case, the presence of two marginally relevant ϕ 6 coupling constants and one ϕ 4 super-renormalizable interaction spoils this interesting property. However, the existence of a non-trivial fixed point is established in dimension 4 − ε, hence suggesting that the SU(2) theory might be asymptotically safe. To pave the way to future non-perturbative calculations, the present perturbative results are discussed in the framework of the effective average action.

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Section: Discussionmentioning

confidence: 99%

Group field theory in dimension4−ϵ

Carrozza

2015

Phys. Rev. D

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“…The FRG approach has been applied first to matrix models [42][43][44] (with the double scaling critical point reinterpreted as a fixed point in the RG flow). More recently, the FRG framework has been adapted and applied for the first time to TGFTs in [45].…”

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confidence: 99%

Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

Geloun

Martini

Oriti

2015

EPL

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-We study a model of Tensorial Group Field Theory (TGFT) on R 3 from the point of view of the Functional Renormalisation Group. This is the first attempt to apply a renormalisation procedure to a TGFT model defined over a non-compact group manifold. IR divergences (with respect to the metric on R) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken. We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.Introduction. -Group Field Theories [1-5] (GFTs) are a particular class of quantum field theories with fields defined over a group manifold and characterised by combinatorially non-local interaction terms. This combinatorial non-locality makes the Feynman diagrams of the theory stranded diagrams dual to cellular complexes (simplicial complexes in the simplest constructions) [1,3]. GFT's historically were born from an attempt to generalise matrix models [6] of 2d gravity to higher dimensions in the form of tensor models [7][8][9]. These models were soon enriched with group theoretic data in such a way that the Feynman amplitudes of specific GFT models coincide with state sum models of topological field theory [9,10]. A connection between GFTs and Loop Quantum Gravity (LQG) [11,12] was immediately pointed out [13] at the level of quantum states, and later enforced at the level of the quantum dynamics. In fact, it was later shown [14] that GFTs provide a formal (complete) definition of spin foams models, a covariant formalism for LQG. For GFTs (and spin foam models) endowed with a discrete geometric interpretation (which requires appropriate group theoretic data and suitable choices of dynamics) there is also a direct link with simplicial quantum gravity path integrals, first manifested in the semiclassical analysis of GFT Feynman (spin foam) amplitudes, where one recovers the Regge action [15], and then shown to be generically manifest in the flux repre-

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“…To discover a universal scaling limit, we use RG techniques adapted to the discrete setting [39,82], based on the idea in [83]. N serves as our notion of RG scale, with N → ∞ constituting the limit of infinitely many degrees of freedom, i.e., the UV limit.…”

Section: Functional Renormalization Group Techniques For Tensor Mmentioning

confidence: 99%

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

Eichhorn

Lumma

Pereira

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...

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Towards phase transitions between discrete and continuum quantum spacetime from the renormalization group

Cited by 49 publications

References 110 publications

Group field theory in dimension4−ϵ

Group field theory in dimension4−ϵ

Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

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

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