arXiv subjects

Norbert Bodendorfer

Publications and source records attributed to Norbert Bodendorfer.

At least 19 recordsLinked to original sources

arXiv2025

A HEART for the environment: Transformer-Based Spatiotemporal Modeling for Air Quality Prediction

Accurate and reliable air pollution forecasting is crucial for effective environmental management and policy-making. llull-environment is a sophisticated and scalable forecasting system for air pollution, inspired by previous models currently operational in Madrid and Valladolid (Spain). It contains (among other key components) an encoder-decoder convolutional neural network to forecast mean pollution levels for four key pollutants (NO$_2$, O$_3$, PM$_{10}$, PM$_{2.5}$) using historical data, external forecasts, and other contextual features. This paper investigates the augmentation of this neural network with an attention mechanism to improve predictive accuracy. The proposed attention mechanism pre-processes tensors containing the input features before passing them to the existing mean forecasting model. The resulting model is a combination of several architectures and ideas and can be described as a "Hybrid Enhanced Autoregressive Transformer", or HEART. The effectiveness of the approach is evaluated by comparing the mean square error (MSE) across different attention layouts against the system without such a mechanism. We observe a significant reduction in MSE of up to 22%, with an average of 7.5% across tested cities and pollutants. The performance of a given attention mechanism turns out to depend on the pollutant, highlighting the differences in their creation and dissipation processes. Our findings are not restricted to optimizing air quality prediction models, but are applicable generally to (fixed length) time series forecasting.

cs.LG↗

arXiv2024

Hamiltonian Theory: generalizations to higher dimensions, supersymmetry and modified gravity

Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction, these properties allow to construct a well defined kinematical quantization of the holonomy flux-algebra on top of which the remaining constraints can be implemented. While this idea has traditionally been mainly used for Einstein gravity, any gravitational theory with the above properties can be accommodated. In this paper, we are going to review three strands of work building on this observation, namely the study of higher-dimensional loop quantum gravity, supersymmetric extensions of loop quantum gravity, as well as the quantization of modified gravitational theories.

gr-qc↗

arXiv2024

Variational Monte Carlo with Neural Network Quantum States for Yang-Mills Matrix Model

We apply the variational Monte Carlo method based on neural network quantum states, using a neural autoregressive flow architecture as our ansatz, to determine the ground state wave function of the bosonic SU($N$) Yang-Mills-type two-matrix model at strong coupling. Previous literature hinted at the inaccuracy of such an approach at strong coupling. In this work, the accuracy of the results is tested using lattice Monte Carlo simulations: we benchmark the expectation value of the energy of the ground state for system sizes $N$ that are beyond brute-force exact diagonalization methods. We observe that the variational method with neural network states reproduces the right ground state energy when the width of the network employed in this work is sufficiently large. We confirm that the correct result is obtained for $N=2$ and $3$, while obtaining a precise value for $N=4$ requires more resources than the amount available for this work.

hep-th↗

arXiv2022

Precision test of gauge/gravity duality in D0-brane matrix model at low temperature

We test the gauge/gravity duality between the matrix model and type IIA string theory at low temperatures with unprecedented accuracy. To this end, we perform lattice Monte Carlo simulations of the Berenstein-Maldacena-Nastase (BMN) matrix model, which is the one-parameter deformation of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model, taking both the large $N$ and continuum limits. We leverage the fact that sufficiently small flux parameters in the BMN matrix model have a negligible impact on the energy of the system while stabilizing the flat directions so that simulations at smaller $N$ than in the BFSS matrix model are possible. Hence, we can perform a precision measurement of the large $N$ continuum energy at the lowest temperatures to date. The energy is in perfect agreement with supergravity predictions including estimations of $\alpha'$-corrections from previous simulations. At the lowest temperature where we can simulate efficiently ($T=0.25\lambda^{1/3}$, where $\lambda$ is the 't Hooft coupling), the difference in energy to the pure supergravity prediction is less than $10\%$. Furthermore, we can extract the coefficient of the $1/N^4$ corrections at a fixed temperature with good accuracy, which was previously unknown.

hep-th↗

arXiv2022

Confinement/deconfinement transition in the D0-brane matrix model -- A signature of M-theory?

We study the confinement/deconfinement transition in the D0-brane matrix model (often called the BFSS matrix model) and its one-parameter deformation (the BMN matrix model) numerically by lattice Monte Carlo simulations. Our results confirm general expectations from the dual string/M-theory picture for strong coupling. In particular, we observe the confined phase in the BFSS matrix model, which is a nontrivial consequence of the M-theory picture. We suggest that these models provide us with an ideal framework to study the Schwarzschild black hole, M-theory, and furthermore, the parameter region of the phase transition between type IIA superstring theory and M-theory. A detailed study of M-theory via lattice Monte Carlo simulations of the D0-brane matrix model might be doable with much smaller computational resources than previously expected.

hep-th↗

arXiv2022

Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model

We test a conjecture by Maldacena and Milekhin for the ungauged version of the Berenstein-Maldacena-Nastase (BMN) matrix model by lattice Monte Carlo simulation. The numerical results reproduce the perturbative and gravity results in the limit of large and small flux parameter, respectively, and are consistent with the conjecture.

hep-th↗

arXiv2021

Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity

A comprehensive study of the application of SO$(D+1)$ coherent states of Perelomov type to loop quantum gravity in general spacetime dimensions $D+1\geq 3$ is given in this paper. We focus on so-called simple representations of SO$(D+1)$ which solve the simplicity constraint and the associated homogeneous harmonic function spaces. With the harmonic function formulation, we study general properties of the coherent states such as the peakedness properties and the inner product. We also discuss the properties of geometric operators evaluated in the coherent states. In particular, we calculate the expectation value of the volume operator, and the results agree with the ones obtained from the classical label of the coherent states up to error terms which vanish in the limit of large representation labels $N$, i.e. the analogue of the large spin limit in standard $3+1$-dimensional loop quantum gravity.

gr-qc↗

arXiv2021

(b,v)-type variables for black to white hole transitions in effective loop quantum gravity

Quantum gravity effects in effective models of loop quantum gravity, such as loop quantum cosmology, are encoded in the choice of so-called polymerisation schemes. Physical viability of the models, such as an onset of quantum effects at curvature scales near the Planck curvature, severely restrict the possible choices. An alternative point of view on the choice of polymerisation scheme is to choose adapted variables so that the scheme is the simplest possible one, known as $μ_0$-scheme in loop quantum cosmology. There, physically viable models with $μ_0$-scheme polymerise the Hubble rate $b$ that is directly related to the Ricci scalar and the matter energy density on-shell. Consequently, the onset of quantum effects depends precisely on those parameters. In this letter, we construct similar variables for black to white hole transitions modelled using the description of the Schwarzschild interior as a Kantowski-Sachs cosmology. The resulting model uses the $μ_0$-scheme and features sensible physics for a broad range of initial conditions (= choices of black and white hole masses) and favours symmetric transitions upon invoking additional qualitative arguments. The resulting Hamiltonian is very simple and at most quadratic in its arguments, allowing for a straight forward quantisation.

gr-qc↗

arXiv2021

Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition

In the past years, black holes and the fate of their singularity have been heavily studied within loop quantum gravity. Effective spacetime descriptions incorporating quantum geometry corrections are provided by the so-called polymer models. Despite the technical differences, the main common feature shared by these models is that the classical singularity is resolved by a black-to-white hole transition. In a recent paper, we discussed the existence of two Dirac observables in the effective quantum theory respectively corresponding to the black and white hole mass. Physical requirements about the onset of quantum effects then fix the relation between these observables after the bounce, which in turn corresponds to a restriction on the admissible initial conditions for the model. In the present paper, we discuss in detail the role of such observables in black hole polymer models. First, we revisit previous models and analyse the existence of the Dirac observables there. Observables for the horizons or the masses are explicitly constructed. In the classical theory, only one Dirac observable has physical relevance. In the quantum theory, we find a relation between the existence of two physically relevant observables and the scaling behaviour of the polymerisation scales under fiducial cell rescaling. We present then a new model based on polymerisation of new variables which allows to overcome previous restrictions on initial conditions. Quantum effects cause a bound of a unique Kretschmann curvature scale, independently of the relation between the two masses.

gr-qc↗

arXiv2021

Partial Deconfinement at Strong Coupling on the Lattice

We provide evidence for partial deconfinement -- the deconfinement of a SU($M$) subgroup of the SU($N$) gauge group -- by using lattice Monte Carlo simulations. We take matrix models as concrete examples. By appropriately fixing the gauge, we observe that the $M\times M$ submatrices deconfine. This gives direct evidence for partial deconfinement at strong coupling. We discuss the applications to QCD and holography.

hep-th↗

arXiv2020

Path integral renormalisation in loop quantum cosmology

A coarse graining technique akin to block spin transformations that groups together fiducial cells in a homogeneous and isotropic universe has been recently developed in the context of loop quantum cosmology. The key technical ingredient was an SU(1, 1) group and Lie algebra structure of the physical observables as well as the use of Perelomov coherent states for SU(1, 1). It was shown that the coarse graining operation is completely captured by changing group representations. Based on this result, it was subsequently shown that one can extract an explicit renormalisation group flow of the loop quantum cosmology Hamiltonian operator in a simple model with dust-clock. In this paper, we continue this line of investigation and derive a coherent state path integral formulation of this quantum theory and extract an explicit expression for the renormalisation-scale dependent classical Hamiltonian entering the path integral for a coarse grained description at that scale. We find corrections to the non-renormalised Hamiltonian that are qualitatively similar to those previously investigated via canonical quantisation. In particular, they are again most sensitive to small quantum numbers, showing that the large quantum number (spin) description captured by so called "effective equations" in loop quantum cosmology does not reproduce the physics of many small quantum numbers (spins). Our results have direct impact on path integral quantisation in loop quantum gravity, showing that the usually taken large spin limit should be expected not to capture (without renormalisation, as mostly done) the physics of many small spins that is usually assumed to be present in physically reasonable quantum states.

gr-qc↗

arXiv2020

A note on coarse graining and group representations

A coarse graining operation of spatially homogeneous quantum states based on an SU(1,1) Lie group structure has recently been proposed in [1] and used in [2] to compute an explicit renormalisation group flow in the context of loop quantum cosmology. In this note, we explain the group theoretical origin of this procedure and generalise previous results based on these insights. We also highlight how the group theoretical origin of these techniques implies their immediate generalisation to other Lie groups.

gr-qc↗

arXiv2020

Renormalisation with SU(1, 1) coherent states on the LQC Hilbert space

We present an analytic computation of an explicit renormalisation group flow for cosmological states in loop quantum gravity. A key ingredient in our analysis are Perelomov coherent states for the Lie group SU(1,1) whose representation spaces are embedded into the standard loop quantum cosmology (LQC) Hilbert space. The SU(1,1) group structure enters our analysis by considering a classical set of phase space functions that generates the Lie algebra su(1,1). We implement this Poisson algebra as operators on the LQC Hilbert space in a non-anomalous way. This task requires a rather involved ordering choice, whose existence is one of the main results of the paper. As a consequence, we can transfer recently established results on coarse graining cosmological states from direct quantisations of the above Poisson algebra to the standard LQC Hilbert space and full theory embeddings thereof. We explicitly discuss how the su(1,1) representation spaces used in this latter approach are embedded into the LQC Hilbert space and how the su(1,1) representation label sets a lower cut-off for the loop quantum gravity spins (= U(1) representation labels in LQC). Our results provide an explicit example of a non-trivial renormalisation group flow with a scale set by the su(1,1) representation label and interpreted as the minimally resolved geometric scale.

gr-qc↗

arXiv2019

Thermal phase transition in Yang-Mills matrix model

We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU($N$) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and this hinders progress in understanding the nature of the black hole/black string topology change from the gauge/gravity duality perspective. On the one hand, previous works considered the deconfinement transition consistent with two transitions which are of second and third order. On the other hand, evidence for a first order transition was put forward more recently. We perform high-statistics lattice Monte Carlo simulations at large $N$ and small lattice spacing to establish that the transition is really of first order. Our findings flag a warning that the required large-$N$ and continuum limit might not have been reached in earlier publications, and that was the source of the discrepancy. Moreover, our detailed results confirm the existence of a new partially deconfined phase which describes non-uniform black strings via the gauge/gravity duality. This phase exhibits universal features already predicted in quantum field theory.

hep-th↗

arXiv2019

Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole

The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches. In the context of loop quantum gravity (LQG), one of the major candidates for a non-perturbative background-independent quantisation of general relativity, considerable effort has been devoted to construct effective models in which these questions can be studied. In these models, classical singularities are replaced by a "bounce" induced by quantum geometry corrections. Undesirable features may arise however depending on the details of the model. In this paper, we focus on Schwarzschild black holes and propose a new effective quantum theory based on polymerisation of new canonical phase space variables inspired by those successful in loop quantum cosmology. The quantum corrected spacetime resulting from the solutions of the effective dynamics is characterised by infinitely many pairs of trapped and anti-trapped regions connected via a space-like transition surface replacing the central singularity. Quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon. The effective quantum metric describes also the exterior regions and asymptotically classical Schwarzschild geometry is recovered. We however find that physically acceptable solutions require us to select a certain subset of initial conditions, corresponding to a specific mass (de-)amplification after the bounce. We also sketch the corresponding quantum theory and explicitly compute the kernel of the Hamiltonian constraint operator.

gr-qc↗

arXiv2019

Holographic signatures of resolved cosmological singularities

The classical gravity approximation is often employed in AdS/CFT to study the dual field theory, as it allows for many computations. A drawback is however the generic presence of singularities in classical gravity, which limits the applicability of AdS/CFT to regimes where the singularities are avoided by bulk probes, or some other form of regularisation is applicable. At the same time, quantum gravity is expected to resolve those singularities and thus to extend the range of applicability of AdS/CFT also in classically singular regimes. This paper exemplifies such a computation. We use an effective quantum corrected Kasner-AdS metric inspired by results from non-perturbative canonical quantum gravity to compute the 2-point correlator in the geodesic approximation for a negative Kasner exponent. The correlator derived in the classical gravity approximation has previously been shown to contain a pole at finite distance as a signature of the singularity. Using the quantum corrected metric, we show explicitly how the pole is resolved and that a new subdominant long-distance contribution to the correlator emerges, caused by geodesics passing arbitrarily close to the resolved classical singularity. In order to compute analytically in this paper, two key simplifications in the quantum corrected metric are necessary. They are lifted in a companion paper using numerical techniques, leading to the same qualitative results.

hep-th↗

arXiv2019

Is limiting curvature mimetic gravity an effective polymer quantum gravity?

A recently proposed version of mimetic gravity incorporates a limiting curvature into general relativity by means of a specific potential depending on the d'Alembertian of the scalar field. In the homogeneous and isotropic setting, the resulting theory agrees with the simplest incarnation of effective loop quantum cosmology (LQC) once the limiting curvature is identified with a multiple of the Planck scale. In this paper, we answer the question of whether such a relation can hold in the context of Bianchi I models. Our result is negative: it turns out to be impossible to view the Hamiltonian of limiting curvature mimetic gravity as an effective LQC Hamiltonian due to the appearance of terms that cannot be supported on the polymer Hilbert space underlying LQC. The present analysis complements a related result in the context of spherical symmetry.

gr-qc↗

arXiv2019

A note on the Hamiltonian as a polymerisation parameter

In effective models of loop quantum gravity, the onset of quantum effects is controlled by a so-called polymerisation scale. It is sometimes necessary to make this scale phase space dependent in order to obtain sensible physics. A particularly interesting choice recently used to study quantum corrected black hole spacetimes takes the generator of time translations itself to set the scale. We review this idea, point out errors in recent treatments, and show how to fix them in principle.

gr-qc↗