October 25 (Mon) *** program of QCD phase diagram and lattice QCD *** all times in JST
-- first session chaired by Hidenori Fukaya --
9:00-9:40 Thomas Cohen University of Maryland
The nature of the high temperature phase of Yang Mills theory: night thoughts on the Polyakov loop
The correlation function of Polyakov loops has traditionally been used to extract a string tension for Yang-Mills theory at non-zero temperature, which vanishes in the high temperature phase. This correlator has long been interpreted in terms of the free energy of static color charges in the fundamental and anti-fundamental representations.  This talk focuses on whether this interpretation is correct and argues that it is based on subtle flaws that render the analysis invalid.  This leads to the possibility that both the high and low temperature phases of Yang-Mills theory should be regarded as confining.
9:40-10:20 Larry McLerran Institute for Nuclear Theory
Quarkyonic and Ghosts
Quarkyonic matter involves both quark degrees of freedom and ghosts.  To avoid double counting, this demands the introduction of nucleonic ghost into an effective quarkyonic matter Lagrangian. In this talk, it is shown how to do this in field theory.
10:20-11:00 Anna Hasenfratz University of Colorado Boulder
From two flavors to twelve: the opening of the conformal window 
Understanding  near-conformal systems is essential for beyond-standard model Composite Higgs models, and also as a theoretical tool to reveal the mechanism conformality arises. In this talk I will discuss results for the renormalization group beta function of SU(3) gauge with zero, two, four, six, eight, ten, and twelve fundamental flavors, from fast running system to conformal ones. Where appropriate, I will contrast staggered and domain wall fermions and also touch on the possibility of determining the anomalous mass dimension in strongly coupled systems.
11:00-11:30 Break @ REMO
-- second session chaired by Anna Hasenfratz --
11:30-11:50 Mamiya Kawaguchi University of Chinese Academy of Sciences
Nonperturbative quark-flavor symmetry breaking in topological susceptibility at hot QCD
The topological susceptibility is a crucial probe in studying the QCD theta-vacuum structure and the axial anomaly. So far, some analyses on the topological susceptibility have been done based on chiral effective models and lattice QCD simulations. However, the flavor independence of the QCD theta-vacuum structure has not been fully taken into account, so that the topological susceptibility in the previous studies would have a lack of the underlying property of QCD (i.e., the flavor singlet nature).
In this talk, we will discuss the thermal property of the topological susceptibility by taking into account the flavor singlet nature. And we will also discuss the quark flavor violation in the topological susceptibility.
11:50-12:10 Yu Zhang RIKEN R-CCS
Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD
In this talk I will present the novel relations between the quark mass derivatives [$partial^n ho(lambda,m_l)/partial m_l^n$] of the Dirac eigenvalue spectrum and the $(n+1)$-point correlations among the eigenvalues. Using these relations we present lattice QCD results for $partial^n ho(lambda,m_l)/partial m_l^n$ ($n=1, 2, 3$) for $m_l$ corresponding to pion masses $m_pi=160-55~$MeV, and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings $a=0.12, 0.08, 0.06$~fm. We find that $ ho(lambda o0,m_l)$ develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as $a o0$, and its amplitude is proportional to $m_l^2$. We demonstrate that this $ ho(lambda o0,m_l)$ is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit. This talk is based on PRL 126 (2021) 082001.
12:10-12:30 Shinichiro Akiyama University of Tsukuba
Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
We analyze the chiral phase transition of the Nambu--Jona-Lasinio model in the cold and dense region on the lattice with the tensor renormalization group algorithm. The model is formulated with the Kogut--Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature on a thermodynamic lattice. We also present the results for the equation of state.
12:30-13:30 Break @ REMO
October 26 (Tue) *** program of QCD phase diagram and lattice QCD *** all times in JST
-- first session chaired by Yasumichi Aoki --
9:00-9:40 Robert Douglas Pisarski Brookhaven National Laboratory
Surprises in the phase diagram of QCD at nonzero density.
I consider several phenomena possible in the phase diagram of QCD at nonzero temperature, T, and chemical potential, mu.  First, the existence of a ''moat'' phase, and possible experimental signatures thereof.  Second, how a Luttinger liquid may emerge in a quarkyonic phase.  Lastly, how the (approximate) restoration of axial U(1) may be very different at high T and low mu, versus low T and high mu.  
9:40-10:20 Edward Shuryak Stony Brook University, USA
Semiclassical theory of deconfinement and chiral phase transitions, in the usual and deformed QCD
Instanton-dyons are topological solutions of YM equations at finite temperatures. Their semiclassical ensembles were studied by a number of methods, including direct Monte-Carlo simulation, for SU(2) and SU(3) theories, with and without fermions. We present these results and compare them with those from lattice studies. We also consider two types of QCD deformations. One is by adding operators with powers of the Polyakov line, affecting deconfinement. Another is changing quark periodicity condition, affecting the chiral transition. Another paper is using inverse direction, from lattice configurations (with realistic quark masses) looking at zero and near-zero Dirac modes. It turned out that those revealing the shape of the modes, In excellent agreement with analytic instanton-dyon theory. Summarizing both we conclude that QCD phase transitions are well described in terms of such semiclassical objects.   
10:20-11:00 Sinya Aoki Yukawa Institute for Theoretical Physics, Kyoto University
Recent rpogress in the HAL QCD method for hadron interactions
We report on recent progress in the HAL method for hadron interactions in lattice QCD, including dibaryon interactions, potential in the moving frame, a study on the derivative expansion and others. 
11:00-11:30 Break @ REMO
-- second session chaired by Hiroshi Suzuki --
11:30-12:10 Masafumi Fukuma Department of Physics, Kyoto University
Numerical sign problem and the tempered Lefschetz thimble method
The numerical sign problem is one of the major obstacles to the first-principles calculations for important physical systems, such as finite-density QCD, strongly-correlated electron systems and frustrated spin systems, as well as for the real-time dynamics of quantum systems. The tempered Lefschetz thimble method (TLTM) [Fukuma and Umeda, 1703.00861] was proposed as a versatile algorithm towards solving the numerical sign problem. There, the integration region is deformed into the complex space according to the antiholomorphic gradient flow equation, and the system is tempered using the flow time as a tempering parameter so as to solve both the sign and ergodicity problems simultaneously. In this talk, I explain the basics of the TLTM, and demonstrate the effectiveness and versatility of the algorithm by showing its successful applications to various models, such as the (0+1)-dimensional massive Thirring model, the Hubbard model away from half filling, and the Stephanov model (a chiral random matrix model). I also would like to explain some of the recent improvements in the algorithm, which is expected to significantly reduce the numerical cost.
12:10-12:30 Takuya Yoda Kyoto University
Quantum phase transition and Resurgence: Lessons from 3d N=4 SQED
Resurgence theory has been studied to uncover non-perturbative aspects of quantum field theories by decoding non-trivial saddle contributions from asymptotic series. We focus on three-dimensional N=4 SQED with multiple hypermultiplets, where a second-order quantum phase transition has been recently reported in the large-flavor limit, to study relations between phase transitions and resurgence. We show that the second-order phase transition is understood as a phenomenon where a Stokes and an anti-Stokes phenomenon co-occur and that the order of the phase transition can be decoded purely from the large-flavor expansion. More general lessons are also drawn from the results in the SQED.
12:30-13:30 Break @ REMO
October 27 (Wed) *** program of QCD phase diagram and lattice QCD *** all times in JST
-- first session chaired by Kazuyuki Kanaya --
16:00-16:40 Masanori Hanada Department of Mathematics, the University of Surrey
Global Symmetries and Partial Deconfinement
In many gauge theories, spontaneous breaking of the center symmetry provides a precise definition of deconfinement. In large-N gauge theories, evidence has emerged recently that between confined and deconfined phases a partially-deconfined phase can appear, in which only a subset of colors deconfine. In the partially-deconfined phase, the center symmetry is spontaneously broken, raising the question of whether an order parameter exists that can distinguish fully- and partially-deconfined phases. We consider two gauge theories in which a global symmetry is spontaneously broken in the confined phase and preserved in the deconfined phase, and we show that this symmetry is spontaneously broken also in the partial phase. As a result, in these theories the transition from full to partial deconfinement is accompanied by the spontaneous breaking of a global symmetry. The two examples are CP symmetry in the minimal super-Yang-Mills with a massive gaugino and theta-angle theta=pi, and chiral symmetry in a strongly-coupled lattice gauge theory. We conjecture that such global symmetries may provide order parameters to distinguish fully- and partially-deconfined phases more generally, including at finite N.

16:40-17:20 Anirban Lahiri Bielefeld University
QCD towards the chiral limit
QCD under extreme conditions has been studied for a long time and the chiral limit has been a grey area mostly. In this talk I will review some of the very recent developments to unveil various features of QCD towards the chiral limit which includes chiral critical temperature, introduction and behaviour of various energy-like observables, possibility of effective restoration of $U_A(1)$ and some preliminary calculations of chiral curvatures.
17:20-18:00 Shinji Takeda Kanazawa University
Study of QCD critical end-point using Wilson-type fermions
It is known that the nature of finite temperature QCD phase transition depends on the number of quark flavors and the value of quark masses. Such a situation is often pictorially summarized as Columbia plot. There is an important and longstanding issue on a structure of the plot, namely a shape of the critical line, which separates first order phase transition region from cross-over region, is not fully determined. In this talk I will review the issue and show our recent lattice QCD simulation results using Wilson-type fermions.
18:00-18:30 Break @ REMO
-- second session chaired by Shinji Takeda --
18:30-19:10 Shoji Hashimoto KEK
Role and subtlety of lattice chiral symmetry in finite temperature QCD
The JLQCD collaboration is performing 2- and 2+1-flavor QCD simulations of finite temperature QCD using domain-wall fermion, Since  the chiral symmetry plays crucial role, we carefully control its violation due to discretization effects, and even introduce a reweighting to the formulation that preserves exact chiral symmetry. We emphasize the crucial role of chiral symmetry in the studies of chiral SU(2)xSU(2) and axial U(1) symmetries.
19:10-19:30 Benjamin Jaeger University of Southern Denmark
The QCD phase diagram with complex Langevin simulations
We present results for the phase diagram of QCD with two light quark flavours at finite chemical potential for a pion mass of 480 MeV. We use the complex Langevin method to deal with the sign problem. We see strong indications of the Silver Blaze phenomenon in our lattice simulation.
19:30-20:00 Break @ REMO
20:00-21:00 -- Poster Session --
1 Gergely Fejos Eotvos University Budapest
Renormalization of field dependent couplings
The importance of considering field dependent couplings in low energy effective theories of the strong interaction is highlighted. Particular emphasis will be put on the renormalization group flows of the Yukawa coupling and that of the axial anomaly in the three flavor quark meson model.
2 Hidenori Fukaya Osaka University
What is chiral susceptibility probing?
In the early days of QCD, the axial $U(1)$ anomaly was considered to trigger the breaking of the $SU(2)_L imes SU(2)_R$ symmetry through topological excitations of gluon fields. However, it has been a challenge for lattice QCD to quantify the effect. In this work, we simulate QCD at high temperatures with the overlap Dirac operator. The exact chiral symmetry enables us to separate the contribution from the axial $U(1)$ breaking from others among the susceptibilities in the scalar and pseudoscalar channels. Our result in two-flavor QCD indicates that the chiral susceptibility, which is conventionally used as a probe for $SU(2)_L imes SU(2)_R$ breaking, is actually dominated by the axial $U(1)$ anomaly at temperatures $Tge 165$ MeV.
3 Issaku Kanamori R-CCS, RIKEN
2+1 Flavor Fine Lattice Simulations for Finite Temperature with Domain Wall Fermions
It is important to keep the chiral symmetry to study the chiral phase transition at finite temperature.  In this talk, I report on-going 2+1 flavor simulation in JLQCD collaboration with stout smeared Moebius Domainwall fermion that keeps almost exact chiral symmetry. The main focus is scanning over temperature between 130 MeV and 205 MeV along the line of constant physics, which uses fixed quark mass in physical unit.

4 Yoshifumi Nakamura RIKEN
Finite temperature phase transition for three flavor QCD with M?bius-domain wall fermions
The nature of the finite temperature phase transition in 2+1 flavor QCD depends on the quark mass, and the order and universal class of the phase transition are shown in a diagram called the Columbia plot.
 The region of light quark masses in this diagram is not yet fully understood. We present preliminary results of a three-flavor QCD study using M?bius-domain wall fermions to search for the critical endpoint in the light quark mass region on the diagonal line of the Columbia plot.
5 Kentaro Nishimura Keio University
Topological term, QCD anomaly, and the η' chiral soliton lattice in rotating baryonic matter
We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η' meson and the QCD anomaly leads to an inhomogeneous condensate of the η' meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η' CSL is much smaller than that for the π0 CSL found previously. We also argue that the η' CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.
6 Felix  Ziegler The University of Edinburgh
Low temperature QCD phase diagram with the complex Langevin method
We present results for the phase diagram of QCD with two light quark flavours at finite chemical potential for a pion mass of 480 MeV. We use the complex Langevin method to deal with the sign problem. We see strong indications of the Silver Blaze phenomenon in our lattice simulations.
October 28 (Thu) *** program of QCD phase diagram and lattice QCD *** all times in JST
-- first session chaired by Yoshifumi Nakamura --
16:00-16:40 Leonid Glozman University of Graz
Three regimes of hot QCD
We introduce a new symmetry in QCD, the chiral spin symmetry, that allows to distinguish the electric and magnetic interactions. Then we discuss its emergence in hadron spectrum upon truncation of the near zero modes of the Dirac operator at T=0. This implies that the chiral symmetry breaking and confinement are not correlated phenomena. It suggests that above a pseudocritical temperature of chiral restoration there should emerge in QCD the chiral spin symmetry, i.e. QCD should be still in the confining regime. This prediction has been tested via a study of symmetry properties of spatial and temporal correlators above Tpc. The chiral spin symmetry is clearly seen in the correlators below roughly T = 500 Mev. Consequently three different regimes should exist in hot QCD. Below Tpc there is a hadron  gas with all symmetries be broken. Above Tpc one arrives at the stringy fluid that is charakterised by both chiral and chiral spin symmetries. Here degrees of freedom are chirally symmetric quarks connected by the electric field into color singlet compounds. At roughly 3 T_pc the color charge and electric field get Debye screened and one observes a very smooth transition to QGP where only chiral symmetries survive. This picture is consistent with the existence of two independent pseudocritical temperatures: the chiral restoration temperature at 155 MeV and center symmetry (''deconfinement'') temperature at 300 MeV.
16:40-17:20 Owe Philipsen Institute for Theoretical Physics, Goethe University Frankfurt
The order of the QCD chiral phase transition for different numbers of quark flavours
The order of the QCD chiral phase transition in the massless limit has been the subject of intense debates and investigations, since it cannot be determined by direct lattice simulations. I present results of an extensive investigation of multiflavour QCD using staggered quarks with different lattice spacings. An analysis employing tricritical scaling to extrapolate to the lattice chiral limit strongly suggests that the continuum phase transition in the massless
limit is of second order for all Nf<7, and possibly up to the conformal window.
17:20-18:00 Maria Paola Lombardo INFN
A new order parameter, and the scaling window of the QCD transition
We study the issue of the universality class of the QCD transition with two massless flavors and for physical values of the strange (and the charm)  masses. We consider different scenarios for the scaling window, assuming that the region dominated by a critical scaling morphs into the mean field domain. The analysis is helped by a new order parameter, free from linear contributions in mass, for which we derive the Equation of State. By contrasting mean field and 3D O(4) critical behavior we identify a scaling window extending up to 300 MeV in temperature, and about 100 MeV in pion mass. These results build further confidence in the 3D O(4) universality class of the chiral transition for the two flavor theory, although alternatives cannot be excluded.
18:00-18:30 Break @ REMO
-- second session chaired by Maria Paola Lombardo --
18:30-19:10 Shinji Ejiri Niigata University
Phase structure of QCD in the heavy quark region
We report a study on the phase transition of QCD in the quark region. We perform simulations of lattice QCD and apply the reweighting method to study the heavy quark region. The quark determinant for the reweighting is evaluated by a hopping parameter expansion. The location of critical point at which the first order phase transition changes to crossover is studied by investigating the histogram of the Polyakov loop and applying the finite-size scaling analysis. The latent heat and pressure gap between the hot and cold phases are also computed at the first order phase transition.
19:10-19:30 Kei Suzuki Japan Atomic Energy Agency
Axial U(1) anomaly at high temperature with chiral fermions
The axial U(1) anomaly in high-temperature QCD plays an important role to understand the phase diagram of QCD. JLQCD Collaboration is studying high-temperature QCD using dynamical chiral fermions such as the domain-wall fermion and reweighted overlap fermion. In this talk, we will present the results for the Dirac spectrum, topological susceptibility, axial U(1) susceptibility, and hadronic collelators.
19:30-20:00 Break @ REMO
October 29 (Fri) *** program of QCD phase diagram and lattice QCD *** all times in JST
-- first session chaired by Atsushi Nakamura --
16:00-16:40 Szabolcs Borsanyi University of Wuppertal
From extrapolation to direct simulations at finite chemical potential
I review some of the extrapolation schemes that are used to extract finite density information from lattice QCD simulations. While the Taylor expansion is well defined and robust, other schemes exist that may converge faster and allow for more cost efficient extrapolations. Finally I will discuss the possibility of simulating lattice QCD at finite mu directly.
16:40-17:20 Masakiyo Kitazawa Osaka University
Stress-energy-momentum tensor on the lattice
I will discuss recent progress in the measurements of the stress-energy-momentum tensor (SEMT) in numerical simulations of the lattice gauge theory. Efficient measurement of SEMT on the lattice has become available recently thanks to the small flow-time expansion (SFTX) method based on the gradient flow. In this talk I will discuss the application of this method for the measurements of thermodynamics in infinite and finite systems, and the local distribution of SEMT in static quark systems.
17:20-18:00 Norikazu Yamada KEK
Peeking into the theta vacuum
We propose a subvolume method to study the $ heta$ dependence of the free energy density of the four-dimensional SU($N$) Yang-Mills theory on  the lattice. As an attempt, the method is first applied to SU(2) Yang-Mills theory at $T=1.2,T_c$ to understand the systematics of the method. We then proceed to the calculation of the vacuum energy density and obtain the $ heta$ dependence, at least, to $ hetasimpi$. The numerical results combined with the theoretical requirements provide the evidence for the spontaneous CP violation at $ heta = pi$, which is in accordance with the large $N$ prediction and in contrast to the CP$^1$ model in two dimensions.
18:00-18:30 Break @ REMO
-- second session chaired by Szabolcs Borsanyi --
18:30-18:50 Andrey Kotov Jülich Forschungszentrum
Phase diagram of rotating gluodynamics and QCD matter
We study the phase diagram of rotating gluodynamics and QCD matter using numerical lattice simulations. Study is performed in the reference frame, which spins with the system, in which rotation is reduced to an external gravitational field. Various types of boundary conditions (open, periodic and Dirichlet) are discussed. We observe that in gluodynamics rotation increases the critical temperature of confinement-deconfinement phase transition, according to a simple quadratic relation T_c(Omega)/T_c(0)=1+C2Omega^2. At the same time first results of the simulations with fermions indicate, that fermionic degrees of freedom under rotation lead to the decrease of the pseudo-critical temperature, contrary to gluons. It suggests, that a careful account of both gluons and fermions is required for the description of the rotating system.
18:50-19:10 Hiroaki Ito Osaka Univ.
One-loop calculation of energy-momentum tensor distribution around a soliton in 1+1d $phi^4$ model 
We investigate the quantum effects on the distribution of energy momentum tensor (EMT) $T_{mu u}(x)$ around a soliton, which is interpreted as the Fourier transform of the form factor, in 1+1d real $phi^4$ theory. We calculate the EMT distribution at the one-loop order and obtain finite results after proper vacuum subtraction and renormalization. The total energy calculated from $T_{00}(x)$ reproduces the known result. We also obtain $T_{11}(x)=0$, which is consistent with the momentum conservation. This result is a natural consequence of the translational invariance that becomes clear by treating the massless mode associated with the translation of the soliton as a collective coordinate. 
19:10-19:30 Yusuke Namekawa Yukawa Institute for Theoretical Physics, Kyoto University
Gauge invariant input to neural network for path optimization method
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)U(1)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.
19:30-20:00 Break @ REMO
20:00-21:00 Conference online dinner / lunch / breakfast @ REMO