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We study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as \textit{thermodynamic geometry}; (iv) the Poincar�� method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first two methods, (i) and (ii), indicate that the entropy of a de Sitter black hole is always in the interval $2/3\leq S\leq 1$, whereas thermodynamic geometry suggests that, at $S=1$, there is a second order phase transition to an Anti de Sitter black hole. On the other hand, we obtain from the Poincar�� method (iv) that black holes whose entropy is $S < 4/3$ are stable or in a saddle-point, whereas when $S>4/3$ they are always unstable, hence there is no definite answer on whether such transition occurs., 13 pages, 6 figures

Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of classical or quantum gravity, of quantum fields in curved space or of other high-energy scenarios, on lower-energy corresponding systems. The ``reverse way'' consists in building fundamental physical theories, for instance, quantum gravity models, inspired by the lower-energy corresponding systems. Here we present the case of graphene and other Dirac materials., Comment: Invited Review, 27 pages, 5 figures. arXiv admin note: text overlap with arXiv:2005.11514

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a [Formula: see text]-oscillator structure, and hence [Formula: see text]-deformed creation/annihilation operators, can be naturally defined on [Formula: see text], which is then mapped into the sum of many copies of the [Formula: see text]-oscillator Hilbert space. This shows that the [Formula: see text]-calculus is a natural calculus for Polymer Quantum Mechanics. Moreover, we show that the inequivalence of different superselected sectors of [Formula: see text] is of topological nature.

Here we briefly resume the idea, originally introduced in Phys. Rev. D 102, 106002 (2020), that the Bekenstein bound on entropy is a consequence of the fermionic nature of fundamental degrees of freedom, which arrange themselves to form matter and spacetime. The main point is discussed by means of a toy-model of black hole evaporation, which describes the dynamics of such degrees of freedom, called Xons. An intrinsic notion of interior/exterior of the black hole during the evaporation process is given and both von Neumann and black hole/environment entropies are computed., 3 pages

We discuss the representations of the algebra of quantization, the canonical commutation relations, in a scalar quantum field theory with spontaneously broken U(1) internal symmetry, when a topological defect of the vortex type is formed via the condensation of Nambu-Goldstone particles. We find that the usual thermodynamic limit is not necessary in order to have the inequivalent representations needed for the existence of physically disjoint phases of the system. This is a new type of inequivalence, due to the nontrivial topological structure of the phase space, that appears at finite volume. We regard this as a first step towards a unifying view of topological and thermodynamic phases, and offer here comments on the possible application of this scenario to quantum gravity., 15 pages, 2 figures

Scientific and practical arguments are offered in favor of a facility where to explore, with analogs, the otherwise unreachable territories of the theoretical investigations on the fundamental components of nature. In this facility, theorists, both of the high-energy and of the condensed matter types, should work next to experimentalists, mostly of the condensed-matter type, and technologists. I call this facility HELIOS, an evocative name for something that should shed light on the darkness of the unknown, and an acronym for High Energy Laboratory for Indirect ObservationS.

We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a $(3+1)$-dimensional theory, with nonzero torsion, with spatiotemporal gauge group $SO(3,1)$, locally isomorphic to the Lorentz group in $(3+1)$ dimensions, or to the de Sitter group in $(2+1)$ dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry with $SU(2)$ internal symmetry. Our results are suggestive, rather than conclusive, and pave the way to the inclusion of grain boundaries in the emergent field theory picture associated with these materials, whereas disclinations and dislocations have been already well explored., Comment: 37 pages, 10 figures, relevant references included, typos corrected

We identify the two-dimensional surfaces corresponding to certain solutions of the Liouville equation of importance for mathematical physics, the non-topological Chern-Simons (or Jackiw-Pi) vortex solutions, characterized by an integer $N \ge 1$. Such surfaces, that we call $S^2 (N)$, have positive constant Gaussian curvature, $K$, but are spheres only when $N=1$. They have edges, and, for any fixed $K$, have maximal radius $c$ that we find here to be $c = N / \sqrt{K} $. If such surfaces are constructed in a laboratory by using graphene (or any other Dirac material), our findings could be of interest to realize table-top Dirac massless excitations on nontrivial backgrounds. We also briefly discuss the type of three-dimensional spacetimes obtained as the product $S^2 (N) \times \mathbb{R}$., 17 pages, 15 figures

To evaluate the effectiveness of the containment on the epidemic spreading of the new Coronavirus disease 2019, we carry on an analysis of the time evolution of the infection in a selected number of different Countries, by considering well-known macroscopic growth laws, the Gompertz law, and the logistic law. We also propose here a generalization of Gompertz law. Our data analysis permits an evaluation of the maximum number of infected individuals. The daily data must be compared with the obtained fits, to verify if the spreading is under control. From our analysis it appears that the spreading reached saturation in China, due to the strong containment policy of the national government. In Singapore a large growth rate, recently observed, suggests the start of a new strong spreading. For South Korea and Italy, instead, the next data on new infections will be crucial to understand if the saturation will be reached for lower or higher numbers of infected individuals., Comment: 8 figures

Assuming dislocations could be meaningfully described by torsion, we propose here a scenario based on the role of time in the low-energy regime of two-dimensional Dirac materials, for which coupling of the fully antisymmetric component of the torsion with the emergent spinor is not necessarily zero. Appropriate inclusion of time is our proposal to overcome well-known geometrical obstructions to such a program, that stopped further research of this kind. In particular, our approach is based on the realization of an exotic $time-loop$, that could be seen as oscillating particle-hole pairs. Although this is a theoretical paper, we moved the first steps toward testing the realization of these scenarios, by envisaging $Gedankenexperiments$ on the interplay between an external electromagnetic field (to excite the pair particle-hole and realize the time-loops), and a suitable distribution of dislocations described as torsion (responsible for the measurable holonomy in the time-loop, hence a current). Our general analysis here establishes that we need to move to a nonlinear response regime. We then conclude by pointing to recent results from the interaction laser-graphene that could be used to look for manifestations of the torsion-induced holonomy of the time-loop, e.g., as specific patterns of suppression/generation of higher harmonics., 24 pages, 5 figures

Strangeness enhancement and collective flow are considered signatures of the quark gluon plasma formation. These phenomena have been detected not only in relativistic heavy ion collisions but also in high energy, high multiplicity events of proton-proton and proton-nucleus (small systems) scatterings. A universal behavior emerges by considering the parton density in the transverse plane as the dynamical quantity to specify the initial condition of the collisions, which in electron-positron annihilation at the available energies is too low to expect collective effects., Comment: 40th International Conference on High Energy physics - ICHEP2020 July 28 - August 6, 2020 Prague, Czech Republic (virtual meeting)

The work of our group on reproducing scenarios of high energy theoretical physics on Dirac materials, like graphene, is illustrated. The main goal of this paper is to explain how versatile these systems are, and how far and wide into the hep-th territory we can explore with them. I first review why these materials lend themselves to the emergence of special relativistic-like matter and space, with the focus on the emergence of curvature. Then the crucial role of the low dimensions (2+1), and Weyl symmetry, towards the realization of a Unruh-kind of phenomenon (along with other interesting scenarios, that include the BTZ black hole and de Sitter spacetime) is explained. Comments on how far we went in the direction of experiments are offered too, followed by a list of some fresh results: From the time-loop to spot torsion, to the generalized uncertainty principle stemming from and underlying (lattice) length; From a model of grain-boundaries and their relation to (A)dS and Poincar\'e spacetime algebras, to Unconventional Supersymmetry and the role of the two Dirac points of graphene; and more. In the concluding remarks I briefly try to make the case for the realization of a ``CERN for analogs'', where theorists. both of the hep-th and of the cond-mat types, sit next to experimentalists, mostly of the cond-mat type., Comment: 14 pages, 3 figures, invited contribution to Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity'' (CORFU2019) 31 August - 25 September 2019, Corf\`u, Greece

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M \neq 0$ Ba\~{n}ados-Teitelboim-Zanelli micro black hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the Generalized Uncertainty Principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell = 1 / \sqrt{-\Lambda}$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario., Comment: v2: 26 pages, 4 figures, accepted for publication in Phys.Rev.D

Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa's Thermofield Dynamics. We then evaluate the von Neumann black hole--environment entropy and noticeably obtain a Page-like evolution. We finally show that this is a consequence of a duality between our model and a quantum dissipative-like fermionic system., Comment: In memory of Martin Scholtz (1984-2019). 10 pages, 3 figures. Matches published version

We propose a scenario where the effects of dislocations, in bidimensional Dirac materials at low energies, can be described within a Dirac field theory by a vertex proportional to the totally antisymmetric component of the torsion generated by such dislocations. The well-known geometrical obstruction to have a nonzero torsion term of that kind in this two-dimensional settings is overcome through exotic time-loops, obtained from ingeniously manipulated particle-hole dynamics. If such torsion/dislocation is indeed present, a net flow of particles-antiparticles (holes) can be inferred and possibly measured. Finally, we comment on how these discoveries pave the way to a laboratory realization on Dirac materials of Unconventional Supersymmetry, as a top-down description of the $\pi$-electrons in backgrounds with a nonzero torsion., Comment: 6 pages, 2 Figures; contribution to the Proceedings of the 40th International Conference on High Energy physics - ICHEP2020, July 28 - August 6, 2020, Prague, Czech Republic (virtual meeting)

Recent experimental results in proton-proton and in proton-nucleus collisions at Large Hadron Collider energies show a strong similarity to those observed in nucleus-nucleus collisions, where the formation of a quark-gluon plasma is expected. We discuss the comparison between small colliding systems and nucleus-nucleus collisions, for: a)~the strangeness suppression factor $\gamma_s$ and yields of multi-strange hadrons; b)~the average transverse momentum, $p_t$, with particular attention to the low $p_t$ region where soft, non-perturbative effects are important; c)~the elliptic flow scaled by the participant eccentricity. The universal behavior in hadronic and nuclear high energy collisions emerges for all these observables in terms of a specific dynamical variable which corresponds to the entropy density of initial system in the collision and which takes into account the transverse size of the initial configuration and its fluctuations., Comment: 5 pages, 4 figures, submitted to journal

Relying on previous results, that link entanglement entropy and parton distribution functions in deep inelastic scattering, and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy, between observed and unobserved degrees of freedom, per nucleon within a nucleus, with respect to the free nucleon. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results.

We show that, by going beyond the low-energy approximation for which the dispersion relations of graphene are linear, the corresponding emergent field theory is a specific generalization a Dirac field theory. The generalized Dirac Hamiltonians one obtains are those compatible with specific generalizations of the uncertainty principle. We also briefly comment on the compatibility of the latter with noncommuting positions, $[x_i,x_j] \neq 0$, and on their possible physical realization., Comment: 11 pages, 1 figure. Work Prepared for the Proceedings of DICE 2018 Workshop held at Toscana, Italy

Within the picture of quark confinement as due to a \textit{color event horizon}, and of hadronization as an instance of the Unruh radiation for the strong force, we show here that QCD entropy, evaluated by lattice simulations in the region $T_c < T < 1.3 T_c$, is in reasonable agreement with a melting color event horizon., 5 pages, 4 figures

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a fundamental minimal length (here graphene lattice spacing) and Lorentz violation (here the particle/hole asymmetry, the trigonal warping, etc.) is naturally obtained. We then show that the corresponding emergent field theory is a table-top realization of such scenarios, by explicitly computing the third order Hamiltonian, and giving the general recipe for any order. Remarkably, our results imply that going beyond the low-energy approximation does not spoil the well-known correspondence with analogue massless quantum electrodynamics phenomena (as usually believed), but rather it is a way to obtain experimental signatures of quantum-gravity-like corrections to such phenomena., Comment: 18 pages, 2 figures, comments added, relevant references included

We provide general arguments regarding the connection between low-energy theories (gravity and quantum field theory) and a hypothetical fundamental theory of quantum gravity, under the assumptions of (i) validity of the holographic bound and (ii) preservation of unitary evolution at the level of the fundamental theory. In particular, the appeal to the holographic bound imposed on generic physical systems by the Bekenstein-Hawking entropy implies that both classical geometry and quantum fields propagating on it should be regarded as phenomena emergent from the dynamics of the fundamental theory. The reshuffling of the fundamental degrees of freedom during the unitary evolution then leads to an entanglement between geometry and quantum fields. The consequences of such scenario are considered in the context of black hole evaporation and the related information-loss issue: we provide a simplistic toy model in which an average loss of information is obtained as a consequence of the geometry-field entanglement., 11 pages, 1 figure, Corfu Summer Institute 2017 'School and Workshops on Elementary Particle Physics and Gravity', 2-28 September 2017, Corfu, Greece

We provide general arguments regarding the connection between low-energy theories (gravity and quantum field theory) and a hypothetical fundamental theory of quantum gravity, under the assumptions of (i) validity of the holographic bound and (ii) preservation of unitary evolution at the level of the fundamental theory. In particular, the appeal to the holographic bound imposed on generic physical systems by the Bekenstein-Hawking entropy implies that both classical geometry and quantum fields propagating on it should be regarded as phenomena emergent from the dynamics of the fundamental theory. The reshuffling of the fundamental degrees of freedom during the unitary evolution then leads to an entanglement between geometry and quantum fields. The consequences of such scenario are considered in the context of black hole evaporation and the related information-loss issue: we provide a simplistic toy model in which an average loss of information is obtained as a consequence of the geometry-field entanglement., 10 pages, 2 figures

We present two lines of reasoning, leading to elementary constituents more fundamental than the ones we know. One such arguments is new, and based on the holographic maximal bound for the number of degrees of freedom of any system. In this case, both matter and space are emergent. The other argument is old, and was given by Richard Feynman as a possible explanation of why analog systems do describe the same physics. The former argument naturally points to a solution of the information paradox. The latter argument elevates analogs from mere curiosities, to reliable tests of fundamental theories. Amusingly, the names given to this fundamental level, both by Feynman and by some of the modern quantum gravity researchers, e.g., Jacob Bekenstein, resemble each others: ``Xons'' (Feynman) vs ``level X'' (Bekenstein)., Comment: 17 pages, 7 figures, invited lecture delivered at Ninth International Workshop DICE2018, September 17-21, 2018 - Castiglioncello (LI) Italy

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two Wess--Zumino $\mathcal{N}=1$ supermultiplets and arguments for its general validity are given. The mechanism relies on the fact that, despite mixing treats fermions and bosons symmetrically, both the fermionic and the bosonic zero point energies are shifted by a positive amount and this kind of shift does not respect supersymmetry., Comment: 5 pages, 1 figure, Eq(12) of V1 corrected to Eq(22), explicit off-shell formulation included, one reference added

We study the influence of a periodic perturbation of the effective masses of the nucleons, due to the assumed semi-classical ultra-light dark matter background, on the motion of neutrons in a gravitational quantum well. Our focus is on the transition probability between the lowest two energy states, with the Rabi frequency in the kHz region corresponding to the series of "sweet spot" dark matter masses in the $10^{-11}$eV ballpark. The relevant probability is written in terms of the specific mass and of the effective coupling to the ordinary matter. These parameters can be constrained by the non-observation of any significant deviations of the measured transition probabilities from the dark-matter-free picture., 6 pages, 2 figures

We model DNA-cation complexes as infinite, one-dimensional, charged wires to single-out the interaction due to quantum fluctuations of the electric field from counterion-induced and water-related interactions. We obtain a frustration-free Casimir-like (codimension 2) interaction that extensive numerical analysis show to be a good candidate to explain the formation and stability of DNA aggregates.

We propose that certain patterns (scars) -- theoretically and numerically predicted to be formed by electrons arranged on a sphere to minimize the repulsive Coulomb potential (the Thomson problem) and experimentally found in spherical crystals formed by self-assembled polystyrene beads (an instance of the {\it generalized} Thomson problem) -- could be relevant to extend the classic Caspar and Klug construction for icosahedrally-shaped virus capsids. The main idea is that scars could be produced on the capsid at an intermediate stage of its evolution and the release of the bending energy present in scars into stretching energy could allow for shape-changes. The conjecture can be tested in experiments and/or in numerical simulations., 13 page, 5 figures

The case for a dedicated laboratory, to test hep-th models on analogue systems, is briefly made. The focus is on graphene., Comment: 3 pages; invited to talk to the workshop "New Frontiers in Multiscale Modelling of Advanced Materials", ECT*, Trento, June 17-20, 2014; to appear in Frontiers in Materials

In this paper we discuss some consequences of cosmological models in which the primordial cosmic matter is described by a relativistic imperfect fluid. The latter takes into account the dissipative effects (bulk viscosity) arising from different cooling rates of the fluid components in the expanding Universe. We discuss, in particular, the effects of the bulk viscosity on Big Bang Nucleosynthesis and on the thermal relic abundance of particles, looking at recent results of PAMELA experiment. The latter has determined an anomalous excess of positron events, that cannot be explained by the conventional cosmology and particle physics., 10 pages

We study the space-time symmetries and transformation properties of the non-commutative U(1) gauge theory, by using Noether charges. We carry out our analysis by keeping an open view on the possible ways $\theta^{\mu \nu}$ could transform. We conclude that $\theta^{\mu \nu}$ cannot transform under any space-time transformation since the theory is not invariant under the conformal transformations, with the only exception of space-time translations. The same analysis applies to other gauge groups., Comment: 6 pages, RevTex

This is a status report about the ongoing work on the realization of quantum field theory on curved graphene spacetimes that uses Weyl symmetry. The programme is actively pursued from many different perspectives. Here we point to what has been done, and to what needs to be done., 82 pages, 19 figures; review. arXiv admin note: substantial text overlap with arXiv:1308.0265

The solutions of many issues, of the ongoing efforts to make deformed graphene a tabletop quantum field theory in curved spacetimes, are presented. A detailed explanation of the special features of curved spacetimes, originating from embedding portions of the Lobachevsky plane into $\mathbf{R}^3$, is given, and the special role of coordinates for the physical realizations in graphene, is explicitly shown, in general, and for various examples. The Rindler spacetime is reobtained, with new important differences with respect to earlier results. The de Sitter spacetime naturally emerges, for the first time, paving the way to future applications in cosmology. The role of the BTZ black hole is also briefly addressed. The singular boundary of the pseudospheres, "Hilbert horizon", is seen to be closely related to event horizon of the Rindler, de Sitter, and BTZ kind. This gives new, and stronger, arguments for the Hawking phenomenon to take place. An important geometric parameter, $c$, overlooked in earlier work, takes here its place for physical applications, and it is shown to be related to graphene's lattice spacing, $\ell$. It is shown that all surfaces of constant negative curvature, ${\cal K} = -r^{-2}$, are unified, in the limit $c/r \to 0$, where they are locally applicable to the Beltrami pseudosphere. This, and $c = \ell$, allow us a) to have a phenomenological control on the reaching of the horizon; b) to use spacetimes different than Rindler for the Hawking phenomenon; c) to approach the generic surface of the family. An improved expression for the thermal LDOS is obtained. A non-thermal term for the total LDOS is found. It takes into account: a) the peculiarities of the graphene-based Rindler spacetime; b) the finiteness of a laboratory surface; c) the optimal use of the Minkowski quantum vacuum, through the choice of this Minkowski-static boundary., Comment: 50 pages, 10 figures; it matches published version (hence is much shorter, has a new abstract, many details are skipped and left to a forthcoming review)

In this contribution we shall present the results about the physics of the top quark by CERN's ATLAS and CMS experiments. After a brief motivation of why it is important to study the top quark at the LHC, we shall discuss the measurement of the production cross sections of top pairs (t t) and single tops. Then, we shall present an overview its properties: mass, avour-changing neutral currents (FCNC), anomalous = E T , resonances and charge asymmetry. The overall agreement with the Standard Model predictions is very good.

A recently proposed step-by-step procedure, to merge the low-energy physics of the $\pi$-bonds electrons of graphene, and quantum field theory on curved spacetimes, is recalled. The last step there is the proposal of an experiment to test a Hawking-Unruh effect, emerging from the model, that manifests itself as an exact (within the model) prediction for the electronic local density of states, in the ideal case of the graphene membrane shaped as a Beltrami pseudosphere. A discussion about one particular attempt to experimentally test the model on molecular graphene is presented, and it is taken as an excuse to solve some basic issues that will help future experiments. In particular, it is stated that the effect should be visible on generic surfaces of constant negative Gaussian curvature, that are infinite in number., Comment: 12 pages, 5 figures, presented at DICE 2012, Castiglioncello - Italy

We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov transformations in terms of operators of the quantum Weyl-Heisenberg algebra. The quantum parameter acts as a label for the unitarily inequivalent representations of the canonical commutation relations in which the space of the states splits in the infinite volume limit., Comment: to appear in Annals of Physics (N.Y.)

In the first attempt to introduce gauge theories in physics, Hermann Weyl, around the 1920s, proposed certain scale transformations to be a fundamental symmetry of nature. Despite the intense use of Weyl symmetry that has been made over the decades, in various theoretical settings, this idea never found its way to the laboratory. Recently, building-up from work by Lochlainn O'Raifeartaigh and collaborators on the Weyl-gauge symmetry, applications of Weyl-symmetry to the electronic properties of graphene have been put forward, first, in a theoretical setting, and later, in an experimental proposal. Here I review those results, by enlarging and deepening the discussion of certain aspects, and by pointing to the steps necessary to make graphene a testing ground of fundamental ideas., Comment: 16 pages, 6 figures; invited talk at the "3rd O'Raifeartaigh Conference on Symmetry and Integrability" 19-21 July, 2012 - Munich, Germany

We find that, for a very specific shape of a monolayer graphene sample, a general relativistic-like description of a back-ground spacetime for graphene's conductivity electrons is very natural. The corresponding electronic local density of states is of finite temperature. This is a Hawking-Unruh effect that we propose to detect through an experiment with a Scanning Tunneling Microscope., 7 pages, 2 figures; insignificant changes to fit the letter format; it matches published version; Physics Letters B (2012)

The experimental detection of the effects of noncommuting coordinates in electrodynamic phenomena depends on the magnitude of |\theta B|, where \theta is the noncommutativity parameter and B a background magnetic field. With the present upper bound on \theta, given by \theta_{\rm bound} \simeq 1/(10 {\rm TeV})^2, there was no large enough magnetic field in nature, including those observed in magnetars, that could give visible effects or, conversely, that could be used to further improve \theta_{\rm bound}. On the other hand, recently it has been proposed that intense enough magnetic fields should be produced at the beginning of relativistic heavy ion collisions. We discuss here lepton pair production by free photons as one kind of signature of noncommutativity and Lorentz violation that could occur at RHIC or LHC. This allows us to obtain a more stringent bound on \theta, given by 10^{-3} \theta_{\rm bound}, if such "exotic" events do not occur., Comment: Five pages, no figures.

The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed., 22 pages, 3 figures - two new references and few typos fixed, matches published version by Annals of Physics