Conformal Anomaly Research Articles

Weyl conformal geometry vs Weyl anomaly

Weyl conformal geometry is a gauge theory of scale invariance that naturally brings together the Standard Model (SM) and Einstein gravity. The SM embedding in this geometry is possible without new degrees of freedom beyond SM and Weyl geometry, while Einstein gravity is generated by the broken phase of this symmetry. This follows a Stueckelberg breaking mechanism in which the Weyl gauge boson becomes massive and decouples, as discussed in the past [1–3]. However, Weyl anomaly could break explicitly this gauge symmetry, hence we study it in Weyl geometry. We first note that in Weyl geometry metricity can be restored with respect to a new differential operator ( hat{nabla} ) that also enforces simultaneously a Weyl-covariant formulation. This leads to a metric-like Weyl gauge invariant formalism that enables one to do quantum calculations directly in Weyl geometry, rather than use a Riemannian (metric) geometry picture. The result is the Weyl-covariance in d dimensions of all geometric operators ( hat{R} , etc) and of their derivatives ( hat{nabla} μ hat{R} , etc), including the Euler-Gauss-Bonnet term. A natural (geometric) Weyl-invariant dimensional regularisation of quantum corrections exists and Weyl gauge symmetry is then maintained and manifest at the quantum level. This is related to a non-trivial current of this symmetry, the divergence of which cancels the trace of the energy-momentum tensor. The “usual” Weyl anomaly and Riemannian geometry are recovered in the (spontaneously) broken phase. The relation to holographic Weyl anomaly is discussed.

Representation of the RG-Invariant Quantities in Perturbative QCD through Powers of the Conformal Anomaly

In this work we consider the possibility of representing the perturbative series for renormalization group invariant quantities in QCD in the form of their decomposition in powers of the conformal anomaly {{beta ({{alpha }_{s}})} mathord{left/ {vphantom {{beta ({{alpha }_{s}})} {{{alpha }_{s}}}}} right. kern-0em} {{{alpha }_{s}}}} in the overline {{text{MS}}} -scheme. We remind that such expansion is possible for the Adler function of the process of {{e}^{ + }}{{e}^{ - }} annihilation into hadrons and the coefficient function of the Bjorken polarized sum rule for the deep-inelastic electron-nucleon scattering, which are both related by the CBK relation. In addition, we study the discussed decomposition for the static quark-antiquark Coulomb-like potential, its relation with the quantity defined by the cusp anomalous dimension and the coefficient function of the Bjorken unpolarized sum rule of neutrino-nucleon scattering. In conclusion we also present the formal results of applying this approach to the non-renormalization invariant ratio between the pole and overline {{text{MS}}} -scheme running mass of heavy quark in QCD and compare them with those already known in the literature. The arguments in favor of the validity of the considered representation in powers of {{beta ({{alpha }_{s}})} mathord{left/ {vphantom {{beta ({{alpha }_{s}})} {{{alpha }_{s}}}}} right. kern-0em} {{{alpha }_{s}}}} for all mentioned renorm-invariant perturbative quantities are discussed.

Quantum effects of the conformal anomaly in a 2D model of gravitational collapse

The macroscopic effects of the quantum conformal anomaly are evaluated in a simplified two-dimensional model of gravitational collapse. The effective action and stress tensor of the anomaly can be expressed in a local quadratic form by the introduction of a scalar conformalon field φ, which satisfies a linear wave equation. A wide class of non-vacuum initial state conditions is generated by different solutions of this equation. An interesting subclass of solutions corresponds to initial states that give rise to an arbitrarily large semi-classical stress tensor leftlangle {T}_{mu}^{nu}rightrangle on the future horizon of the black hole formed in classical collapse. These lead to modification and suppression of Hawking radiation at late times after the collapse, and potentially large backreaction effects on the horizon scale due to the conformal anomaly. The probability of non-vacuum initial conditions large enough to produce these effects is estimated from the Gaussian vacuum wave functional of φ in the Schrödinger representation and shown to be mathcal{O} (1). These results indicate that quantum effects of the conformal anomaly in non-vacuum states are relevant for gravitational collapse in the effective theory of gravity in four dimensions as well.

Anomaly-Induced Quenching of gA in Nuclear Matter and Impact on Search for Neutrinoless ββ Decay

How to disentangle the possible genuine quenching of gA caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor qssb from nuclear correlation effects is described. This is accomplished by matching the Fermi-liquid fixed point theory to the “Extreme Single Particle (shell) Model” (acronym ESPM) in superallowed Gamow–Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for (1−qssb)≠0—that one might identify as “fundamental quenching (FQ)”—in certain experiments seems to be alarmingly significant. I present arguments for how symmetries hidden in the matter-free vacuum can emerge and suppress such FQ in strong nuclear correlations. How to confirm or refute this observation is discussed in terms of the superallowed Gamow–Teller transition in the doubly-magic nucleus 100Sn and in the spectral shape in the multifold forbidden β decay of 115In.

On irregular states and Argyres-Douglas theories

Conformal theories of the Argyres-Douglas type are notoriously hard to study given that they are isolated and strongly coupled thus lacking a lagrangian description. In flat space, an exact description is provided by the Seiberg-Witten theory. Turning on a Ω-background makes the geometry “quantum” and tractable only in the weak curvature limit. In this paper we use the AGT correspondence to derive Ω-exact formulae for the partition function, in the nearby of monopole points where the dynamics is described by irregular conformal blocks of the CFT. The results are checked against those obtained by the recursion relations coming from a conformal anomaly in the region where the two approaches overlap. The Nekrasov-Shatashvili limit is also discussed. Finally, we comment on the existence of black holes in De Sitter space whose low energy dynamics is described by an Argyres-Douglas theory.

Generation of Electric Current by Magnetic Field at the Boundary: Quantum Scale Anomaly Versus Semiclassical Meissner Current Outside of the Conformal Limit

AbstractThe scale (conformal) anomaly can generate an electric current near the boundary of a system in the presence of a static magnetic field. The magnitude of this magnetization current, produced at zero temperature and in the absence of matter, is proportional to a beta function associated with the renormalization of the electric charge. Using first‐principle lattice simulations, this paper investigates how the breaking of the scale symmetry affects this “scale magnetic effect” near a Dirichlet boundary in scalar quantum electrodynamics (Abelian Higgs model). This study demonstrates the interplay of the generated current with vortex excitations both in symmetric (normal) and broken (superconducting) phases and compares the results with the anomalous current produced in the conformal, scale‐invariant regime. Possible experimental signatures of the effect in Dirac semimetals are discussed.

Conformal anomalies in 6D four-derivative theories: A heat-kernel analysis

Conformal anomalies in 6D four-derivative theories: A heat-kernel analysis

Stochastic conformal anomaly detection and resolution for air traffic control

Safety is of the utmost importance in the air traffic system. In recent years, data-driven algorithms have emerged to identify anomalous and potentially unsafe operations based on machine learning techniques. Although many algorithms have shown notable progress in anomaly detection, they have hardly considered the fact that data can be corrupted by noise and uncertainty (e.g., navigation system error) can lead to frequent misdetection and false alarms, which could disturb air traffic controllers and result in system performance degradation. Therefore, an accurate and reliable assessment of emerging safety risks that accounts for and alleviates the effect of uncertainty in data is required for safe and efficient airspace operations. To achieve this goal, this paper proposes a conformal prediction-based framework that explicitly examines uncertainty for reliable anomaly detection and learns online from new streaming data. In addition to supporting the monitoring task of air traffic controllers, the proposed method takes one step forward and provides support for the control task, by offering a resolution strategy when anomaly probability violates the predefined threshold. The proposed method is demonstrated with real air traffic data, called automatic dependent surveillance-broadcast data.

Anomalous Ward identities for on-shell amplitudes at the conformal fixed point

Conformal symmetry underlies many massless quantum field theories, but little is known about the consequences of this powerful symmetry for on-shell scattering amplitudes. Working in a dimensionally-regularised ϕ3 model at the conformal fixed point, we show that the on-shell renormalised amplitudes satisfy anomalous conformal Ward identities. Each external on-shell state contributes two terms to the anomaly. The first term is proportional to the elementary field anomalous dimension, and thus involves only lower-loop information. We show that the second term can be given as the convolution of a universal collinear function and lower-order amplitudes. The computation of the conformal anomaly is therefore simpler than that of the amplitude at the same perturbative order, which gives our anomalous conformal Ward identities a strong predictive power in perturbation theory. Finally, we show that our result is also of practical importance for dimensionally-regularised amplitudes away from the conformal fixed point.

Modular Hamiltonian of the scalar in the semi infinite line: dimensional reduction for spherically symmetric regions

We focus our attention on the one dimensional scalar theories that result from dimensionally reducing the free scalar field theory in arbitrary d dimensions. As is well known, after integrating out the angular coordinates, the free scalar theory can be expressed as an infinite sum of theories living in the semi-infinite line, labeled by the angular modes left{ell, overrightarrow{m}right} . We show that their modular Hamiltonian in an interval attached to the origin is, in turn, the one obtained from the dimensional reduction of the modular Hamiltonian of the conformal parent theory in a sphere. Remarkably, this is a local expression in the energy density, as happens in the conformal case, although the resulting one-dimensional theories are clearly not conformal. We support this result by analyzing the symmetries of these theories, which turn out to be a portion of the original conformal group, and proving that the reduced modular Hamiltonian is in fact the operator generating the modular flow in the interval. By studying the spectrum of these modular Hamiltonians, we also provide an analytic expression for the associated entanglement entropy. Finally, extending the radial regularization scheme originally introduced by Srednicki, we sum over the angular modes to successfully recover the conformal anomaly in the entropy logarithmic coefficient in even dimensions, as well as the universal constant F term in d = 3.

Quantum vacuum effects on the formation of black holes

We study the backreaction of quantum fields induced through the vacuum polarization and the conformal anomaly on the collapse of a thin shell of dust. It is shown that the final fate of the collapse process depends on the physical properties of the shell, including its rest and gravitational masses. Investigating the conditions for the formation of black holes, we notice that quantum effects modify the geometry and structure of Schwarzschild space-time in such a way that black holes have two horizons, an inner and an outer horizon. If the gravitational mass of the shell is about that of an ordinary star, then in most cases, the semi-classical collapse will terminate in a singularity, and in general, quantum fluctuations are not strong enough to prevent the creation of the singularity. Although under certain conditions, it is possible to form a non-singular black hole, i.e., a regular black hole. In this way, the collapse stops at a radius much larger than the Planck length below the inner horizon, and the shell bounces and starts an expansion.

Broken scale invariance and the regularization of a conformal sector in gravity with Wess-Zumino actions

We elaborate on anomaly induced actions of the Wess-Zumino (WZ) form and their relation to the renormalized effective action, which is defined by an ordinary path integral over a conformal sector, in an external gravitational background. In anomaly - induced actions, the issue of scale breaking is usually not addressed, since these actions are obtained only by solving the trace anomaly constraint and are determined by scale invariant functionals. We investigate the changes induced in the structure of such actions once identified in dimensional renormalization (DR) when the ϵ=d−4→0 limit is accompanied by the dimensional reduction (DRed) of the field dependencies. We show that operatorial nonlocal modifications (∼□ϵ) of the counterterms are unnecessary to justify a scale anomaly. In this case, only the ordinary finite subtractions play a critical role in the determination of the scale breaking. This is illustrated for the WZ form of the effective action and its WZ consistency condition, as seen from a renormalization procedure. Logarithmic corrections from finite subtractions are also illustrated in a pure d=4 (cutoff) scheme. The interplay between two renormalization schemes, one based on dimensional regularization (DR) and the second on a cutoff in d=4, illustrates the ambiguities of DR in handling the quantum corrections in a curved background. Therefore, using DR in a curved background, the scale and trace anomalies can both be obtained by counterterms that are Weyl invariant only at d=4.

Ala307Thr variation modulates FSHR structure and impairs its binding affinity for FSH: Implications in polycystic ovarian syndrome.

Follicle-stimulating hormone receptor (FSHR) belongs to the family of G-protein coupled receptors and acts as a cognate receptor for follicle-stimulating hormone (FSH). Among the various polymorphic changes reported in FSHR, rs6165 polymorphism leading to Ala307Thr variation in the extracellular domain of the FSHR (FSHRED ) is widely reported. Therefore we attempted to evaluate the functional implications of this variation by studying its effects on FSHRED structure as well as FSH binding. Our atomic-scale investigations reveal that the hinge region, a key hormone interaction site in the extracellular domain of Wt FSHR, exhibits significantly more flexibility compared with the variant structure. Moreover, the Wt receptor in complex with FSH was observed to form a pocket-like structure in its hinge region whereas such a structure was not detected in the variant. The study further reveals that the key residue, sTyr335, required for FSH recognition and FSHR activation, exhibits lower binding free energy in the variant structure as compared to the Wt. In conclusion, our results point out that Ala307Thr variation leads to structural and conformational anomalies in FSHRED which may alter its FSH binding and affect its activation.

Time-symmetric quantization of relativistic fields. 1. Complex fields, massless gauge fields and gravitons

In the standard formulation of quantum field theory (QFT), where there are only positive energy particles and antiparticles, the energy and charge of the vacuum diverge, which, due to the existence of gravity, leads to the inconsistency of the theory (cosmological constant problem). In the article, it is shown that in the Stueckelberg-Feynman (SF) interpretation, where antiparticles are described as negative energy particles moving backward in time, the zero-point energy and zero-point charge of vacuum of complex fields are absent and there is no cosmological constant problem. However, until now it was believed that the SF interpretation leads to negative probabilities and incompatible with QFT. In the article, it is presented a new formulation of QFT on the basis of the SF interpretation in the form of time-symmetric quantization (TSQ), where the probability of states is positive. In TSQ, the consequences of the SF interpretation are taken into account consecutively and it is shown that: a) the negative sign of the norm of states only changes the sign of the wave function, and not the probabilities; b) the expression of backward in time integrals through the forward in time integrals changes sign; c) the time ordering of the operators is symmetric in time and writing them through the usual ordering leads to the standard diagram technique. For this reason, TSQ correctly describes the known observable effects. In TSQ, the results of unification models change, in particular, a) there is no zero-point energy even with broken supersymmetry between complex fields; b) there is no zero-point energy of modes in string theories, which allows to include gravity, but there is no a conformal anomaly and the dimension of space can be arbitrary.

Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ

We present an analysis of the perturbative realization of the TTJJ correlator, with two stress energy tensors and two conserved currents, using free field theory, integrating out conformal sectors in the quantum corrections. This allows to define, around flat space, an exact perturbative expansion of the complete anomaly effective action – up to 4-point functions – whose predictions can be compared against those of the anomaly induced action. The latter is a variational solution of the conformal anomaly constraint at d=4 in the form of a nonlocal Wess–Zumino action. The renormalization procedure and the degeneracies of the tensor structures of this correlator are discussed, valid for a generic conformal field theory, deriving its anomalous trace Ward identities (WIs). In this application, we also illustrate a general procedure that identifies the minimal number of tensorial structures and corresponding form factors for the TTJJ and any 4-point function. The approach is implemented for three, four and five dimensions, addressing the tensor degeneracies of the expansion in momentum space. We show that the renormalized TTJJ can be split into two contributions, a non anomalous and an anomalous part, each separately conserved. The first satisfies ordinary trace WIs, while the second satisfies anomalous trace WIs. The result of the direct computation is compared against the expression of the same 4-point function derived from the nonlocal anomaly induced action. We show that the prediction for the anomalous part of the TTJJ derived from such action, evaluated in two different conformal decompositions, the Riegert and Fradkin–Vilkovisky (FV) choices, differ from the anomaly part identified in the perturbative TTJJ, in the flat spacetime limit. The anomaly part of the correlator computed with the Riegert choice is affected by double poles, while the one computed with the FV choice does not satisfy the conservation WIs. We present the correct form of the expansion of the anomaly induced action at the second order in the metric perturbations around flat space that reproduces the perturbative result.

Chiral current induced by torsional Weyl anomaly

Torsion can be realized as dislocation in the crystal lattice of material. It is particularly interesting if the material has fermions in the spectrum, such as graphene, topological insulators, and Dirac and Weyl semimetals, as it's transport properties can be affected by the torsion. In this paper, we find that, due to Weyl anomaly, torsion in Dirac and Weyl semimetals can induce novel chiral currents, either near a boundary or in a ``conformally flat space.'' We briefly discuss how to measure this interesting effect in experiment. It is remarkable that these experiments can help to clarify the theoretical controversy of whether an imaginary Pontryagin density could appear in the Weyl anomaly.

Determination of the Electroactive Surface Area of Supported Ir-Based Oxygen Evolution Catalysts by Impedance Spectroscopy: Observed Anomalies with Respect to Catalyst Loading

Recently, several successive papers have proposed a method for determining the actual electrochemically active surface area (ECSA). The method is based on measurements of the impedance response within a suitable potential window and the use of a simple equivalent circuit for the extraction of the so-called adsorption capacity, which is related to the phenomenon of specific adsorption of intermediates in the electrochemical reaction of interest, in particular the oxygen evolution reaction (OER). In this paper, the applicability of the proposed method to the characterization of Ir-based nanostructured electrocatalysts is investigated in more detail. As a model catalyst, we use a commercial sample of Ir nanoparticles dispersed over a high surface area carbon support (Vulcan XC-72). We test the methodology-predicted linear scaling of adsorption capacity with increasing amount (and hence surface area) of catalyst. Systematic experiments are performed with different loadings of the same catalyst. The analysis shows significant deviations from the scaling predicted by the model. To further verify this unexpected result, we extend the analysis to the other model parameters, namely the so-called charge transfer and adsorption resistances and the empirically added double layer capacitance. Interestingly, the analysis shows scaling anomalies only for the first two parameters, which, like the adsorption capacitance, are related to catalytically active sites, but not for the double layer capacitance, which measures the total conductive surface of the studied material. Based on the results, we propose possible reasons for the anomalies and confirm the main hypotheses by impedance simulations using the full physical model - instead of the simplified equivalent circuit.

Real-time detection of deception attacks in cyber-physical systems

AbstractDetection of deception attacks is pivotal to ensure the safe and reliable operation of cyber-physical systems (CPS). Detection of such attacks needs to consider time-series sequences and is very challenging especially for autonomous vehicles that rely on high-dimensional observations from camera sensors. The paper presents an approach to detect deception attacks in real-time utilizing sensor observations, with a special focus on high-dimensional observations. The approach is based on inductive conformal anomaly detection (ICAD) and utilizes a novel generative model which consists of a variational autoencoder (VAE) and a recurrent neural network (RNN) that is used to learn both spatial and temporal features of the normal dynamic behavior of the system. The model can be used to predict the observations for multiple time steps, and the predictions are then compared with actual observations to efficiently quantify the nonconformity of a sequence under attack relative to the expected normal behavior, thereby enabling real-time detection of attacks using high-dimensional sequential data. We evaluate the approach empirically using two simulation case studies of an advanced emergency braking system and an autonomous car racing example, as well as a real-world secure water treatment dataset. The experiments show that the proposed method outperforms other detection methods, and in most experiments, both false positive and false negative rates are less than 10%. Furthermore, execution times measured on both powerful cloud machines and embedded devices are relatively short, thereby enabling real-time detection.

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing Nature. The origin of scales, such as the Higgs vacuum expectation value (vev), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales like the QCD confinement radius are generated by the dilaton vev. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.

Thermodynamics of 5D charged rotating black holes: a counterterms treatment

We use the counterterms subtraction method to calculate various thermodynamical quantities for charged rotating black holes in five-dimensional minimal gauged supergravity (Chong et al. in Phys Rev Lett 95:161301, 2005, https://doi.org/10.1103/PhysRevLett.95.161301, arXiv:hep-th/0506029). Specifically, we analyze certain issues related to the first law and Smarr’s relation in the presence of a conformal anomaly. Among the bulk quantities calculated are the on-shell action, total mass, and angular momenta of the solution. All these quantities are consistent with previous calculations made using other methods. For the boundary theory, we calculate the renormalized stress tensor, conformal anomaly, and Casimir energy. Using the Papadimitriou–Skenderis analysis (Papadimitriou and Skenderis in J High Energy Phys 08:004, 2005), we show that the mass calculated via the counterterms method satisfies the first law of black hole thermodynamics. To discuss extended thermodynamics, we extend the definition of the thermodynamic volume to cases with conformal anomalies using a procedure similar to that of Papadimitriou–Skenderis. We show that this volume correctly accounts for extra terms due to boundary metric variation. This shows that the mass and volume calculated using counterterms satisfy Smarr’s relation as well as the first law.