arXiv subjects

Andreas G. A. Pithis

Publications and source records attributed to Andreas G. A. Pithis.

At least 19 recordsLinked to original sources

arXiv2024

Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives

This collection of perspective pieces captures recent advancements and reflections from a dynamic research community dedicated to bridging quantum gravity, hydrodynamics, and emergent cosmology. It explores four key research areas: (a) the interplay between hydrodynamics and cosmology, including analog gravity systems; (b) phase transitions, continuum limits and emergent geometry in quantum gravity; (c) relational perspectives in gravity and quantum gravity; and (d) the emergence of cosmological models rooted in quantum gravity frameworks. Each contribution presents the distinct perspectives of its respective authors. Additionally, the introduction by the editors proposes an integrative view, suggesting how these thematic units could serve as foundational pillars for a novel theoretical cosmology framework termed "hydrodynamics on superspace".

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arXiv2024

Scalar Cosmological Perturbations from Quantum Gravitational Entanglement

A major challenge at the interface of quantum gravity and cosmology is to explain the emergence of the large-scale structure of the Universe from Planck scale physics. In this letter, we extract the dynamics of scalar isotropic cosmological perturbations from full quantum gravity, as described by the causally complete Barrett-Crane group field theory model. From the perspective of the underlying quantum gravity theory, cosmological perturbations are represented as nearest-neighbor two-body entanglement of group field theory quanta. Their effective dynamics is obtained via mean-field methods and described relationally with respect to a causally coupled physical Lorentz frame. We quantitatively study these effective dynamical equations and show that at low energies they are perfectly consistent with those of General Relativity, while for trans-Planckian scales quantum effects become important. These results therefore not only provide crucial insights into the potentially purely quantum gravitational nature of cosmological perturbations, but also offer rich phenomenological implications for the physics of the early Universe.

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arXiv2024

Scale invariance beyond criticality within the mean-field analysis of tensorial field theories

We continue the series of articles on the application of Landau-Ginzburg mean-field theory to unveil the basic phase structure of tensorial field theories which are characterized by combinatorially non-local interactions. Among others, this class covers tensor field theories (TFT) which lead to a new class of conformal field theories highly relevant for investigations on the AdS/CFT conjecture. Moreover, it also encompasses models within the tensorial group field theory (TGFT) approach to quantum gravity. Crucially, in the infrared we find that the effective mass of the modes relevant for the critical behavior vanishes not only at criticality but also throughout the entire phase of non-vanishing vacuum expectation value due to the non-locality of the interactions. As a consequence, one encounters there the emergence of scale invariance on configuration space which is potentially enhanced to conformal invariance thereon.

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arXiv2024

Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model

It is expected that continuum spacetime emerges via phase transition in the tensorial group field theory (TGFT) approach to quantum gravity. Recent work on the application of Landau-Ginzburg mean-field theory to progressively realistic TGFT models has demonstrated how phase transitions can be realized therein. Here, we further develop this setting and consider the causally complete Lorentzian Barrett-Crane (BC) model which includes not only spacelike but also timelike and lightlike tetrahedra as quantum geometric building blocks. In addition, we incorporate discretized scalar fields by $\mathbb{R}$-valued variables of the group fields. In this context, we analyze models with an arbitrary single interaction of simplicial and tensor-invariant type, extend it to the model with the two vertices well-known from causal dynamical triangulations, and also consider a model with colored simplicial interactions. As a main result, we demonstrate for all those cases that a mean-field approximation of a phase transition towards a non-trivial condensate state can always be realized. In particular, we show that the critical behavior is entirely driven by spacelike faces which are characterized by the boost part of the Lorentz group. The latter induces an exponential suppression of fluctuations which then stabilizes the mean-field vacuum. In contrast, timelike faces do not play a role in this as they are characterized by the rotational and thus compact part of the Lorentz group. Since such a state is typically populated by a large number of TGFT quanta, our work lends further considerable support to the existence of a sensible continuum gravitational regime for causally complete TGFT models. Our results also indirectly strengthen the derivation of effective cosmological dynamics and the recently improved study of scalar cosmological perturbations within a mean-field approximation.

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arXiv2024

Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity

We derive the dynamics of (isotropic) scalar perturbations from the mean-field hydrodynamics of full Lorentzian quantum gravity, as described by a two-sector (timelike and spacelike) Barrett-Crane group field theory (GFT) model. The rich causal structure of this model allows us to consistently implement in the quantum theory the causal properties of a physical Lorentzian reference frame composed of four minimally coupled, massless, and free scalar fields. Using this frame, we are able to effectively construct relational observables that are used to recover macroscopic cosmological quantities. In particular, small isotropic scalar inhomogeneities emerge as a result of (relational) nearest-neighbor two-body entanglement between degrees of freedom of the underlying quantum gravity theory. The dynamical equations we obtain for geometric and matter perturbations show agreement with those of classical general relativity in the long-wavelength, super-horizon limit. In general, deviations become important for sub-horizon modes, which seem to be naturally associated with a trans-Planckian regime in our physical reference frame. We argue that these trans-Planckian corrections are quantum gravitational in nature. However, we explicitly show that for some physically interesting solutions these quantum gravity effects can be quite small, leading to a very good agreement with the classical GR behavior.

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arXiv2023

QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization

Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic potential approximation of a tensorial field theory on the $r$-dimensional torus it was recently shown using functional renormalization group techniques that no such phase transition to a condensate phase with a tentative continuum geometric interpretation is possible. Here, keeping the same approximation, we show how to overcome this limitation amending the theory by local degrees freedom on $\mathbb{R}^d$. We find that the effective $r-1$ dimensions of the torus part dynamically vanish along the renormalization group flow while the $d$ local dimensions persist up to small momentum scales. Consequently, for $d>2$ one can find a phase structure allowing also for phase transitions.

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arXiv2023

Mean-field phase transitions in TGFT quantum gravity

Controlling the continuum limit and extracting effective gravitational physics are shared challenges for quantum gravity approaches based on quantum discrete structures. The description of quantum gravity in terms of tensorial group field theory (TGFT) has recently led to much progress in its application to phenomenology, in particular cosmology. This application relies on the assumption of a phase transition to a nontrivial vacuum (condensate) state describable by mean-field theory, an assumption that is difficult to corroborate by a full renormalization group flow analysis due to the complexity of the relevant TGFT models. Here we demonstrate that this assumption is justified due to the specific ingredients of realistic quantum geometric TGFT models: combinatorially non-local interactions, matter degrees of freedom and Lorentz group data together with the encoding of micro-causality. This greatly strengthens the evidence for the existence of a meaningful continuum gravitational regime in group-field and spin-foam quantum gravity, the phenomenology of which is amenable to explicit computations in a mean-field approximation.

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arXiv2023

Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models

In the tensorial group field theory (TGFT) approach to quantum gravity, the basic quanta of the theory correspond to discrete building blocks of geometry. It is expected that their collective dynamics gives rise to continuum spacetime at a coarse grained level, via a process involving a phase transition. In this work we show for the first time how phase transitions for realistic TGFT models can be realized using Landau-Ginzburg mean-field theory. More precisely, we consider models generating 4-dimensional Lorentzian triangulations formed by spacelike tetrahedra whose quantum geometry is encoded in non-local degrees of freedom on the non-compact group $\mathrm{SL}(2,\mathbb{C})$ and subject to gauge and simplicity constraints. Further we include $\mathbb{R}$-valued variables which may be interpreted as discretized scalar fields typically employed as a matter reference frame. We apply the Ginzburg criterion finding that fluctuations around the non-vanishing mean-field vacuum remain small at large correlation lengths regardless of the combinatorics of the non-local interaction validating the mean-field theory description of the phase transition. This work represents a first crucial step to understand phase transitions in compelling TGFT models for quantum gravity and paves the way for a more complete analysis via functional renormalization group techniques. Moreover, it supports the recent extraction of effective cosmological dynamics from TGFTs in the context of a mean-field approximation.

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arXiv2022

The Complete Barrett-Crane Model and its Causal Structure

The causal structure is a quintessential element of continuum spacetime physics and needs to be properly encoded in a theory of Lorentzian quantum gravity. Established spin foam (and tensorial group field theory (TGFT)) models mostly work with relatively special classes of Lorentzian triangulations (e.g. built from spacelike tetrahedra only), obscuring the explicit implementation of the local causal structure at the microscopic level. We overcome this limitation and construct a full-fledged model for Lorentzian quantum geometry the building blocks of which include spacelike, lightlike and timelike tetrahedra. We realize this within the context of the Barrett-Crane TGFT model. Following an explicit characterization of the amplitudes via methods of integral geometry, and the ensuing clear identification of local causal structure, we analyze the model's amplitudes with respect to its (space)time-orientation properties and provide also a more detailed comparison with the framework of causal dynamical triangulations (CDT).

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arXiv2022

Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model

We study the cosmological sector of the Lorentzian Barrett-Crane (BC) model coupled to a free massless scalar field in its Group Field Theory (GFT) formulation, corresponding to the mean-field hydrodynamics obtained from coherent condensate states. The relational evolution of the condensate with respect to the scalar field yields effective dynamics of homogeneous and isotropic cosmologies, similar to those previously obtained in $\text{SU}(2)$-based EPRL-like models. Also in this manifestly Lorentzian setting, in which only continuous $\text{SL}(2,\mathbb{C})$-representations are used, we obtain generalized Friedmann equations that generically exhibit a quantum bounce, and can reproduce all of the features of the cosmological dynamics of EPRL-like models. This lends support to the expectation that the EPRL-like and BC models may lie in the same continuum universality class, and that the quantum gravity mechanism producing effective bouncing scenarios may not depend directly on the discretization of geometric observables.

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arXiv2021

Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom

In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition. On a compact group of fixed volume this can be expected to be only possible in a large-volume or thermodynamic limit. Here we show how phase transitions are possible in TGFTs in two cases: a) considering the non-local group degrees of freedom on a non-compact Lie group instead of a compact one (or taking a large-volume limit of a compact group); b) in models including $\mathbb{R}$-valued local degrees of freedom (that can be interpreted as discrete scalar fields, often used in this context to provide a matter reference frame). After adapting the Landau-Ginzburg approach to this setting of mixed local/non-local degrees of freedom, we determine the critical dimension beyond which there is a Gaussian fixed point and a continuous phase transition which can be described by mean-field theory. This is an important step towards the realization of a phase transition to continuum spacetime in realistic TGFT models for quantum gravity.

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arXiv2020

Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models

In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition. However, understanding the phase diagram and finding fixed points under the renormalization group flow remains a major challenge. In this work we tackle the issue for a tensorial group field theory using the functional renormalization group method. We derive the flow equation for the effective potential at any order restricting to a subclass of tensorial interactions called cyclic melonic and projecting to a constant field in group space. For a tensor field of rank $r$ on U$(1)$ we explicitly calculate beta functions and find equivalence with those of O$(N)$ models but with an effective dimension flowing from $r-1$ to zero. In the $r-1$ dimensional regime, the equivalence to O$(N)$ models is modified by a tensor specific flow of the anomalous dimension with the consequence that the Wilson-Fisher type fixed point solution has two branches. However, due to the flow to dimension zero, fixed points describing a transition between a broken and unbroken phase do not persist and we find universal symmetry restoration. To overcome this limitation, it is necessary to go beyond compact configuration space.

hep-th↗

arXiv2020

The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization

At criticality, discrete quantum-gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional renormalization group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with $ABAB$-interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality and subjecting the technique to another strong test of its performance in discrete quantum gravity by comparing to known results.

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arXiv2020

(No) phase transition in tensorial group field theory

Continuum spacetime is expected to emerge via phase transition in discrete approaches to quantum gravity. A promising example is tensorial group field theory but its phase diagram remains an open issue. The results of recent attempts in terms of the functional renormalization group method remain inconclusive since they are restricted to truncations of low order. We overcome this barrier with a local-potential approximation for $\textrm{U}(1)$ tensor fields at arbitrary rank $r$ focusing on a specific class of so-called cyclic-melonic interactions. Projecting onto constant field configurations, we obtain the full set of renormalization-group flow equations. At large cut-offs we find equivalence with $r-1$ dimensional $\textrm{O}(N)$ scalar field theory in the large-$N$ limit, modified by a tensor-specific, relatively large anomalous dimension. However, on small length scales there is equivalence with the corresponding scalar field theory with vanishing dimension and, thus, no phase transition. This is confirmed by numerical analysis of the full non-autonomous equations where we always find symmetry restoration. The essential reason for this effect are isolated zero modes. This result should therefore be true for tensor field theories on any compact domain and including any tensor-invariant interactions. Thus, group field theories with non-compact degrees of freedom will be necessary to describe a phase transition to continuum spacetime.

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arXiv2019

Aspects of quantum gravity

For more than 80 years theoretical physicists have been trying to develop a theory of quantum gravity which would successfully combine the tenets of Einstein's theory of general relativity (GR) together with those of quantum field theory. At the current stage, there are various competing responses to this challenge under construction. Attacking the problem of quantum gravity from the quantum geometry perspective, where space and spacetime are discrete, the focus of this thesis lies on the application of loop quantum gravity (LQG) and group field theory (GFT). We employ these two closely related nonperturbative approaches to two areas where quantum gravity effects are broadly expected to be relevant: black holes and quantum cosmology. Concerning black holes, apart from understanding their inner structure, a pressing issue is to give a microscopic explanation for the phenomenon of black hole entropy in terms of a discrete quantum geometry and relate it to the symmetries of the horizon. Black hole models in LQG are typically constructed via the isolated horizon boundary condition which gives rise to an effective description of the horizon geometry in terms SU(2) Chern-Simons theory. In this thesis we find a reinterpretation of the statistics of the horizon degrees of freedom as those of a system of non-Abelian anyons. As regards quantum cosmology, the challenge is to understand how the initial singularity problem of GR can be resolved by means of the discreteness of geometry and how a continuum spacetime can emerge from a large assembly of geometric building blocks. Most recent research in GFT aims at deriving the effective dynamics for condensate states directly from the microscopic GFT quantum dynamics and subsequently to extract a cosmological interpretation from them. In this thesis we elaborate on aspects of this approach and study phenomenological consequences in detail.

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arXiv2018

Phase transitions in group field theory: The Landau perspective

In various approaches to quantum gravity continuum spacetime is expected to emerge from discrete geometries through a phase transition. In group field theory, various indications for such a transition have recently been found but a complete understanding of such a phenomenon remains an open issue. In this work, we investigate the critical behavior of different group field theory models in the Gaussian approximation. Applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation breaks down in the case of three-dimensional Euclidean quantum gravity as described by the dynamical Boulatov model on the compact group $\text{SU}(2)$. This result is independent of the peculiar gauge symmetry and specific form of nonlocality of the model. On the contrary, we find that the Gaussian approximation is valid for a rank-$1$ GFT on the noncompact sector of fields on $\text{SL}(2,\mathbb{R})$ related to Lorentzian models. Though a nonperturbative analysis is needed to settle the question of phase transitions for compact groups, the results may also indicate the necessity to consider group field theory on noncompact domains for phase transitions to occur.

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arXiv2018

Minimizers of the dynamical Boulatov model

We study the Euler-Lagrange equation of the dynamical Boulatov model which is a simplicial model for 3d Euclidean quantum gravity augmented by a Laplace-Beltrami operator. We provide all its solutions on the space of left and right invariant functions that render the interaction of the model an equilateral tetrahedron. Surprisingly, for a non-linear equation of motion, the solution space forms a vector space. This space distinguishes three classes of solutions: saddle points, global and local minima of the action. Our analysis shows that there exists one parameter region of coupling constants for which the action admits degenerate global minima.

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arXiv2018

Can we detect quantum gravity with compact binary inspirals?

Treating general relativity as an effective field theory, we compute the leading-order quantum corrections to the orbits and gravitational-wave emission of astrophysical compact binaries. These corrections are independent of the (unknown) nature of quantum gravity at high energies, and generate a phase shift and amplitude increase in the observed gravitational-wave signal. Unfortunately (but unsurprisingly), these corrections are undetectably small, even in the most optimistic observational scenarios.

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