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In the framework of modular transformations, we reformulate the recently proposed hadron-quark hybrid model when the imaginary baryonic chemical potential is introduced. As a result, we can consider the torus, which is characterized by the complex number densities of baryons (antibaryons) and quarks (antiquarks). We apply this model to analyze the Roberge-Weiss transition. It is shown that the torus vanishes at the baryonic chemical potential where the Roberge-Weiss transition appears because the number density of baryons (antibaryons) is not linearly independent of the number density of quarks (antiquarks). When the temperature T is lower than the Roberge-Weiss transition temperature TRW, the torus shrinks smoothly to the one-dimensional object at the Roberge-Weiss transition point, but the discontinuity does not appear. On the other hand, the discontinuity of the geometrical object appears when T>TRW. We also calculate the modulus of the torus and transform it into the fundamental region. The transformed moduli are symmetric below TRW, but the symmetry is broken above TRW., Comment: 9 pages and 11 figures. (v2) The last paragraph in Sec.5 has been improved. (v3) Some sentences have been revised. one reference has been added

We study chiral condensate in cold nuclear matter on the basis of holographic theory, which would be dual to a baryon system in quantum chromodynamics (QCD) in the confinement phase. Our model is a holographic model based on the D$3$/D$7$ branes. The magnitude of the chiral condensate obtained in our model is found to gradually increase with increasing baryon density $n$ within the range of the dilute nucleon gas, $n<1$, where our model is available. This is a result for the chiral condensate in the holographic model as a function of $n$, which can be compared to the chiral perturbation theory., Comment: 12 pages, 5 figures

We discuss the role of Roberge-Weiss periodicity in the thermodynamics of quantum chromodynamics at moderately high temperature, where the semi-quark-gluon plasma is expected. From the construction of the grand canonical partition function at zero and also at finite density via the canonical approach, we can discuss the relation between contributions of the Polyakov-loop phase and Roberge-Weiss periodicity. Then, we can conclude that the existence of Roberge-Weiss periodicity is a necessary condition to reproduce exact results at moderately high temperature., Comment: 7 pages, 1 figure

Quantum chromodynamics (QCD) with pure imaginary baryon number chemical potential mu =i theta T, where T is temperature and theta is a real number, has the Roberge-Weiss periodicity. We study the theta-dependence of the baryon number density and the pressure in the hadron resonance gas model with excluded volume effects of baryons. It is shown that the baryon number density and the pressure are smooth periodic functions of theta at low or high temperature. However, they have singular behavior at theta =(2k+1)pi where k is an integer, when T sim 211MeV. This temperature is consistent with the Roberge-Weiss transition temperature TRW obtained by lattice QCD simulations. This singularity can be explained by the dual excluded volume effects in which the roles of point-like and non point-like particles are exchanged each other in the ordinary excluded volume effects. It is also indicated that the excluded volume effect is visible just below TRW and is directly detectable by the lattice QCD simulation at finite theta. We compare the results with the one obtained by the Polyakov-loop extended Nambu-Jona-Lasinio model., Comment: 11page, 17figures. (In the revised version, four references and some sentences have been added. )

Choreographic programming (CP) is an emerging paradigm for programming distributed applications that run on multiple nodes. In CP, the programmer writes one program, called a choreography, that is then transformed to individual programs for each node via a compilation step called endpoint projection (EPP). While CP languages have existed for over a decade, library-level CP -- in which choreographies are expressed as programs in an existing host language, and choreographic language constructs and EPP are provided entirely by a host-language library -- is in its infancy. Library-level CP has great potential, but existing implementations have portability, efficiency, and practicality drawbacks that hinder its adoption. In this paper, we aim to advance the state of the art of library-level CP with two novel techniques for choreographic library design and implementation: endpoint projection as dependency injection (EPP-as-DI), and choreographic enclaves. EPP-as-DI is a language-agnostic technique for implementing EPP at the library level. Unlike existing library-level approaches, EPP-as-DI asks little from the host language -- support for higher-order functions is all that is required -- making it usable in a wide variety of host languages. Choreographic enclaves are a language feature that lets the programmer define sub-choreographies within a larger choreography. Within an enclave, "knowledge of choice" is propagated only among the enclave's participants, enabling the seamless use of the host language's conditional constructs while addressing the efficiency limitations of existing library-level CP implementations. We implement EPP-as-DI and choreographic enclaves in ChoRus, the first CP library for the Rust programming language. Our case studies and benchmarks demonstrate that the usability and performance of ChoRus compares favorably to traditional distributed programming in Rust.

A simple phenomenological hybrid hadron-quark model with effective volume effects of baryons and chiral dynamics is investigated. The hybrid EoS naturally connects the low density baryonic matter with the high density quark matter. In the intermediate region, the phase which can not be regarded as pure hadron matter or pure quark matter appears. In this model, there is a possibility that the abrupt first -order like transition to pure quark matter induces the strong chiral symmetry restoration and the speed of sound has a large peak at considerable large density., Comment: 10 pages, 23 figures. (4 figures and some sentences have been newly added by the replacement. )

The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization method is applied by replacing the spins with dynamical variables via the Hubbard-Stratonovich transformation, and the sum with the integral. The one-dimensional (Lenz-)Ising model with a complex coupling constant is used as a laboratory for the sign problem in the spin model. The average phase factor is enhanced by the path optimization method, indicating that the method can weaken the sign problem. Our result reproduces the analytic values with controlled statistical errors., Comment: 8 pages, 5 figures, version accepted for publication in Phys. Rev. D

We present a major new version of Scenic, a probabilistic programming language for writing formal models of the environments of cyber-physical systems. Scenic has been successfully used for the design and analysis of CPS in a variety of domains, but earlier versions are limited to environments which are essentially two-dimensional. In this paper, we extend Scenic with native support for 3D geometry, introducing new syntax which provides expressive ways to describe 3D configurations while preserving the simplicity and readability of the language. We replace Scenic's simplistic representation of objects as boxes with precise modeling of complex shapes, including a ray tracing-based visibility system that accounts for object occlusion. We also extend the language to support arbitrary temporal requirements expressed in LTL, and build an extensible Scenic parser generated from a formal grammar of the language. Finally, we illustrate the new application domains these features enable with case studies that would have been impossible to accurately model in Scenic 2., Comment: 13 pages, 6 figures. Full version of a CAV 2023 tool paper, to appear in the Springer Lecture Notes in Computer Science series

CTA (Cherenkov Telescope Array) is the next generation ground-based observatory for gamma-ray astronomy at very-high energies. The Large-Sized Telescope prototype (LST-1) is located at the Northern site of CTA, on the Canary Island of La Palma. LSTs are designed to provide optimal performance in the lowest part of the energy range covered by CTA, down to $\simeq 20$ GeV. LST-1 started performing astronomical observations in November 2019, during its commissioning phase, and it has been taking data since then. We present the first LST-1 observations of the Crab Nebula, the standard candle of very-high energy gamma-ray astronomy, and use them, together with simulations, to assess the basic performance parameters of the telescope. The data sample consists of around 36 hours of observations at low zenith angles collected between November 2020 and March 2022. LST-1 has reached the expected performance during its commissioning period - only a minor adjustment of the preexisting simulations was needed to match the telescope behavior. The energy threshold at trigger level is estimated to be around 20 GeV, rising to $\simeq 30$ GeV after data analysis. Performance parameters depend strongly on energy, and on the strength of the gamma-ray selection cuts in the analysis: angular resolution ranges from 0.12 to 0.40 degrees, and energy resolution from 15 to 50%. Flux sensitivity is around 1.1% of the Crab Nebula flux above 250 GeV for a 50-h observation (12% for 30 minutes). The spectral energy distribution (in the 0.03 - 30 TeV range) and the light curve obtained for the Crab Nebula agree with previous measurements, considering statistical and systematic uncertainties. A clear periodic signal is also detected from the pulsar at the center of the Nebula., Comment: Accepted in ApJ. v3: updated author list and acknowledgements, fixed typos and other minor issues

We study a holographic model of quantum chromodynamics, which can describe a color superconductor and a dilute nucleon gas phase. The two phases are adjoined in the phase diagram at a critical value of the chemical potential. In other words, a first-order transition from the ordinary nucleon gas to the color superconductor is found by increasing the chemical potential. This model is suitable to investigate the possibility of a cold compact star with a color superconducting core. The equation of state of the star is given by the holographic model considered in this article, and we find that it is impossible in the present model to find a hybrid star of nuclear matter and the color superconductor core through the relation of mass and radius of the star by solving the Tolman-Oppenheimer-Volkoff equations. Several other interesting implications are given by using the equation of state., Comment: 22 pages, 10 figures, version accepted for publication in PRD. Title changed following the referee's suggestion

Choreographic programming is an emerging paradigm for programming distributed systems. In choreographic programming, the programmer describes the behavior of the entire system as a single, unified program -- a choreography -- which is then compiled to individual programs that run on each node, via a compilation step called endpoint projection. We present a new model for functional choreographic programming where choreographies are expressed as computations in a monad. Our model supports cutting-edge choreographic programming features that enable modularity and code reuse: in particular, it supports higher-order choreographies, in which a choreography may be passed as an argument to another choreography, and location-polymorphic choreographies, in which a choreography can abstract over nodes. Our model is implemented in a Haskell library, HasChor, which lets programmers write choreographic programs while using the rich Haskell ecosystem at no cost, bringing choreographic programming within reach of everyday Haskellers. Moreover, thanks to Haskell's abstractions, the implementation of the HasChor library itself is concise and understandable, boiling down endpoint projection to its short and simple essence.

We investigate efficiency of a gauge-covariant neural network and an approximation of the Jacobian in optimizing the complexified integration path toward evading the sign problem in lattice field theories. For the construction of the complexified integration path, we employ the path optimization method. The $2$-dimensional $\text{U}(1)$ gauge theory with the complex gauge coupling constant is used as a laboratory to evaluate the efficiency. It is found that the gauge-covariant neural network, which is composed of the Stout-like smearing, can enhance the average phase factor, as the gauge-invariant input does. For the approximation of the Jacobian, we test the most drastic case in which we perfectly drop the Jacobian during the learning process. It reduces the numerical cost of the Jacobian calculation from ${\cal O}(N^3)$ to ${\cal O}(1)$, where $N$ means the number of degrees of freedom of the theory. The path optimization using this Jacobian approximation still enhances the average phase factor at expense of a slight increase of the statistical error., Comment: 8 pages, 5 figures; accepted version

We investigate the efficiency of a gauge invariant input to a neural network for the path optimization method. While the path optimization with a completely gauge-fixed link-variable input has successfully tamed the sign problem in a simple gauge theory, the optimization does not work well when the gauge degrees of freedom remain. We propose to employ a gauge invariant input, such as plaquette, to overcome this problem. The efficiency of the gauge invariant input to the neural network is evaluated for the 2-dimensional $U(1)$ gauge theory with a complex coupling. The average phase factor is significantly enhanced by the path optimization with the plaquette input, indicating good control of the sign problem. It opens a possibility that the path optimization is available to complicated gauge theories, including Quantum Chromodynamics, in a realistic setup., Comment: 7 pages, 8 figures; published version

At sufficiently low temperature, without requiring any numerical data at finite real chemical potential, we can clarify the canonical partition function with fixed quark number via the imaginary chemical potential region with few ansatzs. The canonical partition function relates to the multiplicity distribution which can be observed in collider experiments and thus we may access important information of the properties of the QCD matter based on the canonical method. In this paper, we estimate the multiplicity entropy, the configuration entropy, and the pointwise information which can be calculable with the canonical partition function to understand the properties of the cold QCD matter at finite density. With the large $N_\mathrm{c}$ limit where $N_\mathrm{c}$ is the number of colors, we can simply estimate the tendency of them, and then the relation to the quarkyonic phase is clarified. In addition, we discuss the nontrivial ground state degeneracy from the viewpoint of the canonical sectors., Comment: 11pages

In a holographic model, which was used to investigate the color superconducting phase of QCD, a dilute gas of instantons is introduced to study the nuclear matter. The free energy of the nuclear matter is computed as a function of the baryon chemical potential in the probe approximation. Then the equation of state is obtained at low temperature. Using the equation of state for the nuclear matter, the Tolman-Oppenheimer-Volkov equations for a cold compact star are solved. We find the mass-radius relation of the star, which is similar to the one for quark star. This similarity implies that the instanton gas given here is a kind of self-bound matter., Comment: 19 pages, 3 figures

The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure of zeros of the microscopic probability density function at the nonanalytic point. The average value of the Polyakov line can detect the structure, while the other thermodynamic quantities are not sensible to the structure in the zero-temperature limit. The effect of the imaginary quark chemical potential is also discussed. The imaginary part of the quark number density is very sensitive to the symmetry structure at the nonanalytical point. For a particular value of the imaginary quark number chemical potential, large quark number may be induced in the vicinity of the nonanalytical point., Comment: 14pages, 25figures

The isospin chemical potential region is known as the sign-problem free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic the dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it as QCD-like Potts model. The QCD-like Potts model does not have the sign problem, but we can expect that it shares some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential where the simple Metropolis algorithm can work, we perform the persistent homology analysis towards exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition., Comment: 10 pages, 10 figures

We investigate the nuclear and the quark matter at finite real chemical potential ($\mu_\mathrm{R}$) and low temperature from the viewpoint of the canonical sectors constructed via the imaginary chemical potential region. Based on the large $N_\mathrm{c}$ estimation, where $N_\mathrm{c}$ is the number of color, we can discuss the confinement-deconfinement nature at finite $\mu_\mathrm{R}$ from the canonical sectors. We found the expectation that the sharp change of canonical sectors at $\mu_\mathrm{R} \sim M_\mathrm{B}/N_\mathrm{c}$, where $M_\mathrm{B}$ is the lowest baryon mass, is happen in the large $N_\mathrm{c}$ regime, and it is matched with the quarkyonic picture. In addition, we discussed the color superconductivity and the chiral properties from the structure of canonical sectors. Even in the present anatomy from the canonical sectors, we can have the suitable picture for the dense QCD matter., Comment: 9 pages, 1 figure

To understand the phase transition phenomena, information theoretical approaches can pick up some important properties of the phenomena based on the probability distribution. In this paper, we show information theoretical aspects of the 3-dimensional 3-state Potts model with the external field which is corresponding to the QCD effective model with heavy quarks. The transfer mutual information which represents the information flow of two spin variables is numerically estimated based on the Markov-chain Monte-Carlo method. The transfer mutual information has the peak near the confinement-deconfinement transition, and it may be used to detect the precursors of the transition. Since the transfer mutual information still have the peak even if the Polyakov-loop changes continuously and smoothly, we may pick up some aspects of the confinement-deconfinement nature from the information flow properties. Particularly, the transfer mutual information shows the significantly different behavior below and above the Roberge-Weiss endpoint existed in the pure imaginary chemical potential region, which may indicate the system change by the confinement-deconfinement transition., Comment: 8 pages, 3 figures

In this article, we apply the path optimization method to handle the complexified parameters in the 1+1 dimensional pure $U(1)$ gauge theory on the lattice. Complexified parameters make it possible to explore the Lee-Yang zeros which helps us to understand the phase structure and thus we consider the complex coupling constant with the path optimization method in the theory. We clarify the gauge fixing issue in the path optimization method; the gauge fixing helps to optimize the integration path effectively. With the gauge fixing, the path optimization method can treat the complex parameter and control the sign problem. It is the first step to directly tackle the Lee-Yang zero analysis of the gauge theory by using the path optimization method., Comment: 7 pages, 9 figures

We extend a bottom up holographic model, which has been used in studying the color superconductivity in QCD, to the imaginary chemical potential ($\mu_I$) region, and the phase diagram is studied on the $\mu_I$-temperature (T) plane. The analysis is performed for the case of the probe approximation and for the background where the back reaction from the flavor fermions are taken into account. For both cases, we could find the expected Roberge-Weiss (RW) transitions. In the case of the back-reacted solution, a bound of the color number $N_c$ is found to produce the RW periodicity. It is given as $N_c\geq 1.2$. Furthermore, we could assure the validity of this extended model by comparing our result with the one of the lattice QCD near $\mu_I=0$., Comment: 18 pages, 6 figures

The path optimization has been proposed to weaken the sign problem which appears in some field theories such as finite density QCD. In this method, we optimize the integration path in complex plain to enhance the average phase factor. In this study, we discuss the application of this method to low dimensional QCD as a first step of finite density QCD., Comment: Talk given at the 37th International Symposium on Lattice Field Theory, June 16-22, 2019, Wuhan, China. 7 pages, 9 figures

We discuss the sign problem in the Polyakov loop extended Nambu--Jona-Lasinio model with repulsive vector-type interaction by using the path optimization method. In this model, both of the Polyakov loop and the vector-type interaction cause the model sign problem, and several prescriptions have been utilized even in the mean field treatment. In the path optimization method, integration variables are complexified and the integration path (manifold) is optimized to evade the sign problem, or equivalently to enhance the average phase factor. Within the homogeneous field ansatz, the path is optimized by using the feedforward neural network. We find that the assumptions adopted in previous works, $\mathrm{Re}\,A_8 \simeq 0$ and $\mathrm{Re}\,\omega \simeq 0$, can be justified from the Monte-Carlo configurations sampled on the optimized path. We also derive the Euler-Lagrange equation for the optimal path to satisfy. The two optimized paths, the solution of the Euler-Lagrange equation and the variationally optimized path, agree with each other in the region with large statistical weight., Comment: Talk given at the 37th International Symposium on Lattice Field Theory, June 16-22, 2019, Wuhan, China. 7 pages, 3 figures