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We construct a family of polytopes, which we call Chevalley polytopes, associated to homogeneous spaces $X=G/P$ in their projective embeddings $X\hookrightarrow \mathbb{P}(V_{\varpi})$ together with a choice of reduced expression for the minimal coset representative $w^P$ of $w_0$ in $W/W_P$. When $X$ is minuscule in its minimal embedding, we describe our construction in terms of order polytopes of minuscule posets and use the associated combinatorics to show that minuscule Chevalley polytopes are Newton-Okounkov bodies for $X$ and that the Pl\"ucker coordinates on $X$ form a Khovanskii basis for $\mathbb{C}[X]$. We conjecture similar properties for general $X$ and general embeddings $X\hookrightarrow\mathbb{P}(V_\varpi)$, along with a remarkable decomposition property which we consider as a polytopal shadow of the Littlewood-Richardson rule. We highlight a connection between Chevalley polytopes and string polytopes and give examples where Chevalley polytopes possess better combinatorial properties than string polytopes. We conclude with several examples further illustrating and supporting our conjectures., Comment: 24 pages

We present a type-independent Landau-Ginzburg (LG) model $(X_\mathrm{can}, \mathcal{W}_\mathrm{can})$ for any cominuscule homogeneous space $X=G/P$. We give a fully combinatorial construction for our superpotential $\mathcal{W}_\mathrm{can}$ as a sum of $n+1$ rational functions in the (generalized) Pl\"ucker coordinates on the "Langlands dual" minuscule homogeneous space $\mathbb{X}=P^\vee\backslash G^\vee$. Explicitly, we define the denominators $\mathcal{D}_{i_*}$ of these rational functions using the combinatorics of order ideals of the corresponding minuscule poset, which can be interpreted as (generalized) Young diagrams, by a process that can be described by "moving boxes" and hence is easily implemented. To construct the corresponding numerators, we define derivations $\delta_{i_1}$ on $\mathbb{C}[\mathbb{X}]$ that act by "adding an appropriate box if possible" and then we apply each $\delta_{i_1}$ to the corresponding $\mathcal{D}_{i_*}$. By studying certain Weyl orbits in the fundamental representations of $\widetilde{G}^\vee$ and exploiting the existence of a certain dense algebraic torus in $\mathbb{X}$, we show that the polynomials $\mathcal{D}_{i_*}$ coincide with the generalized minors $\phi_{i_*}$ appearing in the cluster structures for homogeneous spaces studied by Gei\ss-Leclerc-Schr\"oer in arXiv:math/0609138. We then define the mirror variety $X_\mathrm{can}=\mathbb{X}\setminus D_\mathrm{ac}$ to be the complement of the anticanonical divisor $D_\mathrm{ac} = \sum_{i_*}\{\mathcal{D}_{i_*}=0\}$ formed by the $\mathcal{D}_{i_*}$. Moreover, we show that the LG models $(X_\mathrm{can},\mathcal{W}_\mathrm{can})$ are isomorphic to the Lie-theoretic LG-models $(X_\mathrm{Lie},\mathcal{W}_\mathrm{Lie})$ constructed by Rietsch in arXiv:math/0511124 and our models naturally generalize the type-dependent Pl\"ucker coordinate LG-models previously studied by various authors., Comment: 72 pages

We analyze deformations of two-dimensional conformal field theory (CFT) from the perspective of classical bosonic closed string field theory (SFT). The latter can be viewed as a version of Wilsonian renormalization group (RG) improved conformal perturbation theory, where the renormalization scheme is defined through the choice of string vertices in the construction of SFT. Furthermore, the CFT data at the RG fixed point can be recovered from the spectrum and amplitudes of string field fluctuations. As applications, we construct the Horowitz-Polchinski "string star" solution in SFT, and a solution of tachyon-dilaton condensation that deforms the noncompact boson to minimal models by creating a pair of "Runkel-Watts walls"., Comment: 41 pages, 4 figures

In this report we use our methods in arXiv:2204.03548 and its upcoming generalization to complete the construction of canonical mirror models for all cominuscule homogeneous spaces, by considering the maximal orthogonal Grassmannians $\mathrm{OG}(n + 1, 2n + 2)$., Comment: 6 pages, contribution to the proceedings of the 15th international workshop "Lie Theory and its Applications in Physics" (June 2023)

Detecting thermal Unruh radiation from accelerated electrons has presented a formidable challenge due not only to technical difficulties but also for lack of conceptual clarity about what is actually seen by a laboratory observer. We give a summary of the current interpretations along with a simpler heuristic description that draws on the analogy between the Unruh effect and radiation from a two-level atomic system. We propose an experiment to test whether there is emission of thermal photons from an accelerated electron., Comment: This is an expanded version of section 3.2 of arXiv:2211.13187 which we wrote for the Multi Petawatt Prioritization (MP3) workshop. This paper has been accepted for publication in EPJC

The Unruh effect, thereby an ideally accelerated quantum detector is predicted to absorb thermalized virtual photons and re-emit real photons, is significantly extended for laboratory accessible configurations. Using modern influence functional techniques, we obtain explicit expressions describing the excitation and relaxation of the quantum levels of an Unruh detector as a general noninertial open quantum system. Remarkably, for controllable periodical motions, an exact master equation is found for the Unruh detector within the prevailing framework of quantum optics with a well-defined Unruh temperature for given acceleration ($\alpha$), acceleration frequency ($\omega_\alpha$), and transition frequency ($\omega_0$) of the detector. We further show that the measurable Unruh temperatures and corresponding transition rates are comparable or higher than their values for the ideally accelerated cases if $c\omega_0$ and $c\omega_\alpha$ have similar orders of magnitude as $\alpha$. This allows us to select the transition rates of the detector to unmask Unruh radiation against Larmor radiation which has been a major competing noise. Our work suggests experiments with such settings may directly confirm the Unruh effect within the current technology, based on which a laboratory test of black hole thermodynamics will become possible., Comment: 6 pages, 3 figures

We illustrate the relation between supermoduli integration and picture changing operators (PCOs) particularly concerning the role of vertical integration, in the context of superstring vacuum amplitudes, by an explicit comparison of different parameterizations of the supermoduli space of genus two super Riemann surfaces., Comment: 26 pages, 3 figures

We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with insertions of picture changing operators (PCO) on the worldsheet and the vertical integration prescription, by showing how the latter arises from a specific construction of the supermoduli integration contour., Comment: 29 pages, 3 figures; minor revision, reference added

We present projective Landau-Ginzburg models for the exceptional cominuscule homogeneous spaces $\mathbb{OP}^2 = E_6^\mathrm{sc}/P_6$ and $E_7^\mathrm{sc}/P_7$, known respectively as the Cayley plane and the Freudenthal variety. These models are defined on the complement $X^\vee_\mathrm{can}$ of an anti-canonical divisor of the "Langlands dual homogeneous spaces" $\mathbb{X}^\vee = P^\vee\backslash G^\vee$ in terms of generalized Pl\"ucker coordinates, analogous to the canonical models defined for Grassmannians, quadrics and Lagrangian Grassmannians in arXiv:1307.1085, arXiv:1404.4844, arXiv:1304.4958. We prove that these models for the exceptional family are isomorphic to the Lie-theoretic mirror models defined in arXiv:math/0511124 using a restriction to an algebraic torus, also known as the Lusztig torus, as proven in arXiv:1912.09122. We also give a cluster structure on $\mathbb{C}[\mathbb{X}^\vee]$, prove that the Pl\"ucker coordinates form a Khovanskii basis for a valuation defined using the Lusztig torus, and compute the Newton-Okounkov body associated to this valuation. Although we present our methods for the exceptional types, they generalize immediately to the members of other cominuscule families., Comment: 46 pages, 2 figures, code available at https://github.com/foxflo/ExceptionalCominusculeSpaces

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves., Comment: 16 pages, 3 figures, version published in the Special Issue of Symmetry "New Frontiers in Quantum Gravity"

In [RW19] Rietsch and Williams relate cluster structures and mirror symmetry for type A Grassmannians Gr(k, n), and use this interaction to construct Newton-Okounkov bodies and associated toric degenerations. In this article we define a cluster seed for the Lagrangian Grassmannian, and prove that the associated Newton-Okounkov body agrees up to unimodular equivalence with a polytope obtained from the superpotential defined by Pech and Rietsch on the mirror Orthogonal Grassmannian in [PR13]., Comment: 19 pages

Vulnerable road users (VRUs) such as pedestrians, cyclists and motorcyclists are at the highest risk in the road traffic environment. Globally, over half of road traffic deaths are vulnerable road users. Although substantial efforts are being made to improve VRU safety from engineering solutions to law enforcement, the death toll of VRUs' continues to rise. The emerging technology, Cooperative Intelligent Transportation System (C-ITS), has the proven potential to enhance road safety by enabling wireless communication to exchange information among road users. Such exchanged information is utilized for creating situational awareness and detecting any potential collisions in advance to take necessary measures to avoid any possible road casualties. The current state-of-the-art solutions of C-ITS for VRU safety, however, are limited to unidirectional communication where VRUs are only responsible for alerting their presence to drivers with the intention of avoiding collisions. This one-way interaction is substantially limiting the enormous potential of C-ITS which otherwise can be employed to devise a more effective solution for the VRU safety where VRU can be equipped with bidirectional communication with full C-ITS functionalities. To address such problems and to explore better C-ITS solution suggestions for VRU, this paper reviewed and evaluated the current technologies and safety methods proposed for VRU safety over the period 2007-2020. Later, it presents the design considerations for a cellular-based Vehicle-to-VRU (V2VRU) communication system along with potential challenges of a cellular-based approach to provide necessary recommendations., Comment: 16 pages, 5 Figures

We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal class of Ashtekar-Barbero connection variables is constructed, which can be quantized using spin networks. Crucially, the quantum states become separable into the eigen states of the generator of the scale transformation and spin-network states in the Einstein frame. The eigen values consist of additional quantum numbers including a new type of fundamental frequency $\omega$ and energy $E = \hbar \omega$ with respect to a new local time $\tau$ carried by every spin-network vertex. The discretely distributed $\tau$ values as the "quanta of time" correspond to a functional time related to the integrated Weyl current in the classical theory. The Immirzi ambiguity of loop quantum geometry is removed by scale symmetry. To probe the quantum behaviour of the early Universe, the new formalism is applied to a scale-invariant homogenous and isotropic cosmological model coupled to a doublet of scalars with illustrative numerical simulations. The Einstein-frame volume is quantized in recently improved and regularized polymer representations with an arbitrary Immirzi parameter. The resulting unitary evolution of the quantum state of an expanding universe has a positive energy spectrum. A rescaling of the Immirzi parameter is equivalent to a translation in time without changing dynamics. The big bang can be identified in the past time limit when the expectation values of the Jordan-frame volume tend to zero. Remarkably, the quantized big bang is not replaced by a big bounce---a prevalent scenario in present loop quantum cosmology., Comment: 7 pages, 4 figures, version to appear in PLB

Time synchronization in communication networks provides a common time frame among all nodes, thussupporting various network functions such as message transmission, channel scheduling and resourcesharing in real-time and in correct order. In vehicular ad-hoc networks (VANETs) for connected andautomated vehicles, network nodes must be synchronized to exchange time-critical vehicle locationsand warning messages for various road safety applications. However, this is challenging as the datacommunication systems need to achieve low latency and high reliability under the conditions ofhigh user dynamics and density. While many synchronization techniques have been developed forgeneral communications networks, it is necessary to understand the requirements for VANET timesynchronization and the applicability of existing time synchronization techniques in VANET applications.This paper provides a survey on theory and practice of time synchronization in VANETs. It addressessome key factors in VANET time synchronization such as requirements analysis, precision, accuracy,availability, scalability and compatibility, and highlights the advantages of Global Navigation SatelliteSystem (GNSS) in VANET time synchronization. Through this survey, some insights are developed intoexisting and emerging protocols for time synchronization in VANETs., Comment: 13 pages, Vehicular Communications (2018)

This article is an extended version of the peer-reviewed publication; Moffat and Wang, J Phys Math 2018, 9:4 DOI: 10.4172/2090-0902.1000289 The article sets out to address a number of issues concerning Loop Quantum Gravity raised by Ashtekar, such as in a recent post to Arxiv.org (A Ashtekar Arxiv:gr-qc /0702030 v 2.0 May 2007). These include, for example, conditions for the existence of Poincare invariant quantum states. In doing so, this article provides a coherent mathematical framework for both the evolution of space-time and the supersymmetric graviton in the early universe. In this extended form, it is mnhopefully more accessible to research students at the advanced undergraduate level and beginning doctoral level. The key extensions are: a. An explicit cohomology based link between movement across a computational spin network and a dimensioned embedding of the network to produce equivalent movement along a discrete path in space-time; b). A discussion of the implications for quantum ergodic theory and black hole dynamics., Comment: The previous version (v1) remains. Version 2 now appears as arXiv:1612.01018v2

A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general relativity and scale-invariant scalar-tensor and dilaton theories. Consequently, matter to be coupled to such theories is restricted to be conformal or scale invariant. Standard model-type systems naturally fall into this category. The new loop quantization follows from a novel conformally generalized Holst action principle. In contrast to standard loop quantum gravity, the resulting quantum geometry is not beset by the Immirzi ambiguity and has no definitive area gaps within the considered large class of theories of gravitation. As an additional feature, the scale invariance gives rise to a conserved Weyl current and we discuss briefly its possible implication on the problem of time in quantum gravity., Comment: 35 pages (8 pages main text, 27 pages supplementary material); Published version