We discuss the vacuum structure of QCD with two flavors of Wilson fermions. We derive two possible scenarios: (i) If the spectral density $ρ_U(λ,κ)$ of the overlap hamiltonian in a fixed background gauge field is not symmetric in $λ$, Hermiticity is violated and Hermiticity violation effects could influence numerical determinations of the $η$ meson mass if we are not near enough to the continuum limit, where Hermiticity should be recovered; (ii) otherwise we argue that, under certain assumptions, new phases appear beside the Aoki phase, which can be characterized by a nonvanishing vacuum expectation value of $i\barψ_uγ_5ψ_u+i\barψ_dγ_5ψ_d$, and with vacuum states that cannot be connected with the Aoki vacua by parity-flavor symmetry transformations. Quenched numerical simulations suggest that the second scenario is more likely realized.
We report on a numerical reinvestigation of the Aoki phase in full lattice QCD with two flavors of unimproved Wilson fermions. For zero temperature the Aoki phase can be confirmed at inverse coupling $β=4.0$ and $β=4.3$, but not at $β=4.6$ and $β=5.0$. At non-zero temperature the Aoki phase was found to exist also at $β=4.6$.
In this letter we report on a numerical investigation of the Aoki phase in the case of finite temperature which continues our former study at zero temperature. We have performed simulations with Wilson fermions at $β=4.6$ using lattices with temporal extension $N_τ=4$. In contrast to the zero temperature case, the existence of an Aoki phase can be confirmed for a small range in $κ$ at $β=4.6$, however, shifted slightly to lower $κ$. Despite fine-tuning $κ$ we could not separate the thermal transition line from the Aoki phase.
We investigate the parity-broken phase (Aoki phase) for staggered-Wilson fermions by using the Gross-Neveu model and the strong-coupling lattice QCD. In the both cases the gap equations indicate the parity-broken phase exists and the pion becomes massless on the phase boundaries. We also show we can take the chiral and continuum limit in the Gross-Neveu model by tuning mass and gauge-coupling parameters. This supports the idea that the staggered-Wilson fermions can be applied to the lattice QCD simulation by taking a chiral limit, as with Wilson fermions.
We study strong-coupling lattice QCD with staggered-Wilson fermions, with an emphasis on the possibility of spontaneous parity breaking. We perform effective potential analysis in the strong-coupling limit. From gap equations we find the pion condensate becomes nonzero in some range of a mass parameter, which indicates the existence of the parity-broken phase. We also find massless pions and PCAC relations around the second-order phase boundary. These results suggest that we can take the chiral limit by tuning a mass parameter in lattice QCD with staggered-Wilson fermions as with the Wilson fe…
In this paper, we discuss the vacuum structure of QCD with two flavors of Wilson fermions, inside the Aoki phase. We provide numerical evidence, coming from HMC simulations in $4^4$, $6^4$ and $8^4$ lattices, supporting a vacuum structure for this model at strong coupling more complex than the one assumed in the standard wisdom, with new vacua where the expectation value of $i\barψγ_5ψ$ can take non-zero values, and which can not be connected with the Aoki vacua by parity-flavour symmetry transformations.
The vacuum structure of QCD with two degenerated flavours of Wilson fermions is discussed by means of the p.d.f. (probability distribution function) formalism. Under certain assumptions, either new phases related to Aoki's appear, characterized by a non-vanishing expectation value of the condensate $i\barψ_uγ_5ψ_u + i\barψ_dγ_5ψ_d$, enriching the standard picture of the QCD vacuum structure with Wilson fermions; or the eigenvalues of the Dirac-Wilson operator must comply with a non-trivial, infinite set of sum rules, enforcing the currently accepted structure of the Aoki vacuum. The same scena…
We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\barψ i γ_{5} τ^{3}ψ$ was added to the fermion action. The order parameter $<\barψ i γ_{5}τ^{3}ψ>$ was computed with the Hybrid Monte Carlo algorithm at several values of $(β,κ,h)$ on lattices of sizes $4^4$ to $12^4$ and extrapolated to $h=0$. The existence of a parity-flavor breaking phase can be confirmed at $β=4.0$ and 4.3, while we do not find parity-flavor brea…
The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero lattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a systematic expansion in the quark mass, the momentum and $a^2$. Starting from this chiral Lagrangian we obtain an analytical expression for the spectral density of $γ_5 (D_W+m)$ in the microscopic domain. It is shown that the $γ_5$-Hermiticity of the Dirac operator necessarily leads to a coefficient of the $a^2$ term that is consistent with the existence of an Aoki phase. The transition to the Aoki phase is explained, and the interplay of the ind…
Lattice QCD with two flavors of Wilson fermions can exhibit spontaneous breaking of flavor and parity, with the resulting "Aoki phase" characterized by the non-zero expectation value $<\barψγ_5 τ_3 ψ>\ne0$. This phenomenon can be understood using the chiral effective theory appropriate to the Symanzik effective action. Within this standard analysis, the flavor-singlet pseudoscalar expectation value vanishes: $<i \barψγ_5 ψ>=0$. A recent reanalysis has questioned this understanding, arguing that either the Aoki-phase is unphysical, or that there are additional phases in which $<i \barψγ_5 ψ>\ne…
We construct the effective field theory appropriate for describing the low energy behavior of anisotropic Wilson lattice actions and the O(a) improved variant thereof. We then apply this effective field theory to the hadron spectrum and dispersion relations, focussing on the corrections due to the anisotropy. We point out an important feature of anisotropic lattices regarding the Aoki-regime; for a given set of fermion masses and spatial lattice spacing, if an isotropic action is in the QCD-phase, this does not guarantee that the anisotropic action is outside the Aoki-regime. This may be impor…
In order to elucidate the vacuum structure of the Aoki phase, we carried out a numerical investigation of QCD with two flavours of Wilson fermions, within the p.d.f. framework and in the absence of external sources. The simulations performed at V = 44 suggest a rich vacuum structure, where the observable $i\barψγ_5ψ$ is allowed to take non-zero values of the same order of magnitude than the order parameter of the Aoki phase $i\barψγ_5τ_3ψ$. However, the simulation at higher volumes V = 6^4 suffers from large statistical errors.
We discuss the phase diagram of Wilson fermions in the $m_0$--$g^2$ plane for two-flavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken ``Aoki phase''. We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional term…
In this talk we determine the phase diagram and pion spectrum for Wilson and twisted-mass fermions in the presence of non-degeneracy between the up and down quark and discretization errors. We find that the CP-violating phase of the continuum theory, which occurs for sufficiently large non-degeneracy, is continuously connected to the Aoki phase found in the lattice theory with degenerate quarks. Both for the Aoki and first-order scenarios, this results in a critical surface along which at least one of the pions is massless. In the pion spectrum, we focus mainly on the untwisted case, where the…
When Anderson localization takes place in a quenched disordered system, a continuous symmetry can be broken spontaneously without accompanying Goldstone bosons. Elaborating on this observation we propose a unified, microscopic physical picture of the phase diagram of both quenched and unquenched QCD with two flavors of Wilson fermions. The phase with Goldstone bosons -- by definition the Aoki phase -- is always identified as the region where the mobility edge of the (hermitian) Wilson operator is zero. We then discuss the implications for domain-wall and overlap fermions. We conclude that both…
At nonzero lattice spacing the QCD partition function with Wilson quarks undergoes either a second order phase transition to the Aoki phase for decreasing quark mass or shows a first order jump when the quark mass changes sign. We discuss these phase transitions in terms of Wilson Dirac spectra and show that the first order scenario can only occur in the presence of dynamical quarks while in the quenched case we can only have a transition to the Aoki phase. The exact microscopic spectral density of the non-Hermitian Wilson Dirac operator with dynamical quarks is discussed as well. We conclude …
I conjecture on the phase structure expected for lattice gauge theory with two flavors of Wilson fermions, concentrating on large values of the hopping parameter. Numerous phases are expected, including the conventional confinement and deconfinement phases, as well as an Aoki phase with spontaneous breaking of flavor and parity and a large hopping phase corresponding to negative quark masses.
We discuss the symmetries of quenched QCD with Wilson fermions, starting from its lagrangian formulation, taking into account the constraints needed for convergence of the ghost-quark functional integral. We construct the corresponding chiral effective lagrangian, including terms linear and quadratic in the lattice spacing. This allows us to study the phase structure of the quenched theory, and compare it to that in the unquenched theory. In particular we study whether there may be an Aoki phase (with parity and flavor spontaneously broken) or a first order transition line (with no symmetry br…
We present first results of a study of two flavour QCD with Wilson fermions at finite temperature. We have used tree level Symanzik improvement in both the gauge and fermion part of the action. In a first step we explore the phase diagramm on an $8^3 \times 4$ lattice, with particular emphasis on checking Aoki's conjecture with an improved action.
In this paper, we examine the phase diagram of quenched QCD with two flavors of Wilson fermions, proposing the following microscopic picture. The super-critical regions inside and outside the Aoki phase are characterized by the existence of a density of near-zero modes of the (hermitian) Wilson-Dirac operator, and thus by a non-vanishing pion condensate. Inside the Aoki phase, this density is built up from extended near-zero modes, while outside the Aoki phase, there is a non-vanishing density of exponentially localized near-zero modes, which occur in "exceptional" gauge-field configurations. …
This work is concerned with the phase diagram of Wilson fermions in the mass and coupling constant plane for two-flavor (unquenched) QCD. We show that as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian, supplemented by additional terms proportional to powers of the lattice spacing. We find two possible phase structures at non-zero lattice spacing: (1) There is an Aoki phase of spontaneously broken flavor and parity, with two massless Goldstone-pions, and a width $Δm_0 \sim a^3$; (2) There is no spontaneous symmetry breaking, and all thr…
We present results of an ongoing study of two flavour QCD with Wilson fermions at finite temperature. We have used tree level Symanzik improvement in both the gauge and fermion part of the action. The phase diagram was previously determined on an $8^3 \times 4$ lattice and the existence of Aoki's phase demonstrated. On our current lattice of $12^2 \times 24 \times 4$ we have extended the set of observables and studied chiral and thermal properties at light quark masses.
The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism…
We investigate the limit of vanishing quark mass in quenched lattice QCD with unimproved Wilson fermions at $β=6.0$. Exploiting the correlations of propagators at different time slices we extract pion masses extremely close to the `chiral limit', despite the presence of `exceptional configurations'. With this at hand, the existence of quenched chiral logarithms can be demonstrated, provided, finite size effects are small. With reference to the phase diagram proposed by Aoki also the range $κ> κ_c$ is investigated. The width of a potential parity-flavor violating phase can, if at all, hardly be…
We investigate the parity-broken phase structure for staggered and naive fermions in the Gross-Neveu model as a toy model of QCD. We consider a generalized staggered Gross-Neveu model including two types of four-point interactions. We use generalized mass terms to split the doublers for both staggered and naive fermions. The phase boundaries derived from the gap equations show that the mass splitting of tastes results in an Aoki phase both in the staggered and naive cases. We also discuss the continuum limit of these models and explore taking the chirally-symmetric limit by fine-tuning a mass …
In this talk, I reported on recent work on the Aoki phase diagram for quenched QCD with two flavors of Wilson fermions. Part of this work was done in collaboration with Yigal Shamir, and a shorter account of this part appeared recently. In this write-up, I will therefore limit myself to reporting on work done with Steve Sharpe and Robert Singleton, Jr, which has not been published yet. We discuss the symmetries of quenched QCD, paying careful attention to non-perturbative issues. This allows us to derive an effective lagrangian which agrees with standard quenched chiral perturbation theory, bu…
We investigate the phase structure of lattice QCD with dynamical Wilson fermions. Wilson chiral perturbation theory predicts that the Aoki phase and the Sharpe-Singleton scenario manifest themselves in very distinct behavior of the Wilson Dirac eigenvalue spectrum. To test this prediction we perform a direct calculation of the eigenvalues of the non-Hermitian Wilson Dirac operator in dynamical lattice simulations. Moreover, we demonstrate an unexpected quark mass dependence on the shape of the eigenvalue distribution in the positive quark mass side.
We explore aspects of the phase structure of SU(2) and SU(3) lattice gauge theories at strong coupling with many flavours $N_f$ of Wilson fermions in the fundamental representation, including the relevance to recent searches for a conformal window. The pseudoscalar meson mass, the quark mass and other quantities are observed as functions of the hopping parameter, and we find deviations from the expected analytic dependence, at least for sufficiently large $N_f$. Implications of these effects for the phase structure and for the existence of a (first order) bulk phase and the Aoki phase are disc…
We analyze the vacuum structure of a generalized lattice Nambu--Jona-Lasinio model with two flavors of Wilson fermions, such that its continuum action is the most general four-fermion action with 'trivial' color interactions, and having a $SU(2)_V x SU(2)_A$ symmetry in the chiral limit. The phase structure of this model in the space of the two four-fermion couplings shows, in addition to the standard Aoki phases, new phases with $<\barψγ_5ψ> != 0$, in close analogy to similar results recently suggested by some of us for lattice QCD with two degenerate Wilson fermions. This result shows how th…
We present numerical results for the phase diagram of lattice QCD at finite temperature in the formulation with twisted mass Wilson fermions and a tree-level Symanzik-improved gauge action. Our simulations are performed on lattices with temporal extent N_τ=8, and lattice coupling βranging from strong coupling to the scaling domain. Covering a wide range in the space spanned by the lattice coupling βand the hopping and twisted mass parameters κand μ, respectively, we obtain a comprehensive picture of the rich phase structure of the lattice theory. In particular, we verify the existence of an Ao…
We determine the phase diagram and pion spectrum for Wilson and twisted-mass fermions in the presence of non-degeneracy between the up and down quark and discretization errors, using Wilson and twisted-mass chiral perturbation theory. We find that the CP-violating phase of the continuum theory (which occurs for sufficiently large non-degeneracy) is continuously connected to the Aoki-phase of the lattice theory with degenerate quarks. We show that discretization effects can, in some cases, push simulations with physical masses closer to either the CP-violating phase or another phase not present…
We determine the location $λ_c$ of the mobility edge in the spectrum of the hermitian Wilson operator in pure-gauge ensembles with plaquette, Iwasaki, and DBW2 gauge actions. The results allow mapping a portion of the (quenched) Aoki phase diagram. We use Green function techniques to study the localized and extended modes. Where $λ_c>0$ we characterize the localized modes in terms of an average support length and an average localization length, the latter determined from the asymptotic decay rate of the mode density. We argue that, since the overlap operator is commonly constructed from the Wi…
We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter re…
The introduction of a chirally twisted mass term has been proposed as an attractive approach to O(a) improvement of Quantum Chromodynamics with Wilson fermions on a lattice. For numerical simulation projects it is important to know the phase structure of the theory in the region of small quark masses. We study this question in the framework of chiral perturbation theory. Generalizing the analysis of Sharpe and Singleton we find extensions of normal and Aoki phase scenarios and a possible new phase with spontaneous breakdown of chiral symmetry to a discrete $Z_2$.
Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, coherent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. Studies of localization properties of Dirac eigenmodes have also shown evidence for the delocalization of low-lying modes on effectively 3-dimensional surfaces. In this talk, I review some theoretical ideas which suggest the possibility of 3-dimensionally coherent topological charge structur…
In the framework of Wilson Chiral Perturbation Theory, we study the effect induced by a twisted Wilson term, as it appears in Twisted Mass QCD (with 2 degenerate quarks). In particular we consider the vacuum orientation and the pion masses. The computations are done to NLO both in the mass and in the lattice spacing (i.e. to O(a^2)). There are no restrictions on the relative size of lattice artifacts with respect to the physical mass, thus allowing, in principle, to bridge between the physical regime and the unphysical one, where lattice artifacts tend to dominate. The inclusion of O(a^2) latt…
Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group
School of Physics, Renmin University of China（中国人民大学物理学院）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）；Graduate School of Science, The University of Tokyo（东京大学理学研究科）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Key Laboratory of Quantum State Construction and Manipulation of MoE, Renmin University of China（教育部量子态构建与操控重点实验室（中国人民大学））
The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be realized as a overlap of two many body vacua.
We determine the location $λ_c$ of the mobility edge in the spectrum of the hermitian Wilson operator on quenched ensembles. We confirm a theoretical picture of localization proposed for the Aoki phase diagram. When $λ_c>0$ we also determine some key properties of the localized eigenmodes with eigenvalues $|λ|<λ_c$. Our results lead to simple tests for the validity of simulations with overlap and domain-wall fermions.
The microscopic spectral density of the Wilson Dirac operator for two flavor lattice QCD is analyzed. The computation includes the leading order a^2 corrections of the chiral Lagrangian in the microscopic limit. The result is used to demonstrate how the Sharpe-Singleton first order scenario is realized in terms of the eigenvalues of the Wilson Dirac operator. We show that the Sharpe-Singleton scenario only takes place in the theory with dynamical fermions whereas the Aoki phase can be realized in the quenched as well as the unquenched theory. Moreover, we give constraints imposed by gamma_5-He…
We discuss the use of Wilson fermions with twisted mass for simulations of QCD thermodynamics. As a prerequisite for a future analysis of the finite-temperature transition making use of automatic O(a) improvement, we investigate the phase structure in the space spanned by the hopping parameter kappa, the coupling beta, and the twisted mass parameter mu. We present results for N_f=2 degenerate quarks on a 16^3x8 lattice, for which we investigate the possibility of an Aoki phase existing at strong coupling and vanishing mu, as well as of a thermal phase transition at moderate gauge couplings and…
We consider the phase diagram of twisted mass Wilson fermions of two-flavor QCD in the parameter space of the quark mass, the isospin chemical potential, the twist angle and the lattice spacing. This work extends earlier studies in the continuum and those at zero chemical potential. We evaluate the phase diagram as well as the spectrum of the (pseudo-)Goldstone bosons using the chiral Lagrangian for twisted mass Wilson fermions at non-zero isospin chemical potential. The phases are obtained from a mean field analysis. At zero twist angle we find that already an infinitesimal isospin chemical p…
We use the effective chiral Lagrangian to analyze the phase diagram of two-flavor twisted mass lattice QCD as a function of the normal and twisted masses, generalizing previous work for the untwisted theory. We first determine the chiral Lagrangian including discretization effects up to next-to-leading order (NLO) in a combined expansion in which m_π^2/(4πf_π)^2 ~ a Λ(a being the lattice spacing, and Λ= Λ_{QCD}). We then focus on the region where m_π^2/(4πf_π)^2 ~ (a Λ)^2, in which case competition between leading and NLO terms can lead to phase transitions. As for untwisted Wilson fermions, w…
We develop the $(1+1)$d lattice $U(1)$ gauge theory in order to define $2$-flavor massless Schwinger model, and discuss its connection with Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, as $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{\bar{V}}$, prohibits the additive mass renormalization. Moreover, we show that Dirac determinant is positive s…
The Hypercube operator determines a variant of the approximate, truncated perfect fermion action. In this pilot study we are going to report on first experiences in dynamical QCD simulations with the Hypercube fermions. We apply this formulation in an investigation of the finite temperature transition for two flavours. On lattices of size $8^3\times 4$ we explore the phase diagram. Physical scales are estimated from pseudoscalar and vector meson masses obtained on $8^3\times 16$ lattices. We observe the presence of a metastability region but do not find evidence for an Aoki phase. The Hypercub…
Topological invariants for the 4D gapped system are discussed with application to the quantum vacua of relativistic quantum fields. Expression $\tilde{\cal N}_3$ for the 4D systems with mass gap defined in \cite{Volovik2010} is considered. It is demonstrated that $\tilde{\cal N}_3$ remains the topological invariant when the interacting theory in deep ultraviolet is effectively massless. We also consider the 5D systems and demonstrate how 4D invariants emerge as a result of the dimensional reduction. In particular, the new 4D invariant $\tilde{\cal N}_5$ is suggested. The index theorem is prove…
D-theory provides an alternative lattice regularization of the (1+1)-d CP(N-1) quantum field theory. In this formulation the continuous classical CP(N-1) fields emerge from the dimensional reduction of discrete SU(N) quantum spins. In analogy to Haldane's conjecture, ladders consisting of an even number of transversely coupled spin chains lead to a CP(N-1) model with vacuum angle θ= 0, while an odd number of chains yields θ= π. In contrast to Wilson's formulation of lattice field theory, in D-theory no sign problem arises at θ= π, and an efficient cluster algorithm is used to investigate the θ…
In most Yang-Mills models the vacuum where magnetic monopoles condense coincides with that where center vortices percolate, thus it is not clear which of these two properties is most directly involved in producing confinement. It is pointed out that there is a class of 3D gauge models, which can be though of as duals of Q-state Potts models with Q < 1, where the magnetic monopole condensation is a necessary but not sufficient condition for percolation of center vortices. A set of numerical tests at Q=1/10 shows that there is a vacuum in which the magnetic monopole condensate does not yield con…
We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a^2), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a^2) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying…
Detailed information of the low-energy interaction between the charmonia (ηc and J/ψ) and the nucleon is indispensable for exploring the formation of charmonium bound to nuclei. In order to investigate the charmonium-nucleon interactions at low energies, we adopt two essentially different approaches in lattice QCD simulations. The charmonium-nucleon potential can be calculated from the equal-time Bethe-Salpeter amplitude through the effective Schrödinger equation. This novel method is based on the same idea originally applied for the nucleon force by Aoki- Hatsuda-Ishii. Another approach is to…
Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a Berry connection, which is a gauge connection obtained from the phase of the electron wave function transported over momentum space rather than coordinate space. The phase of a closed Wilson loop of the Berry connection around the Brillouin zone defines a topological order parameter which labels discrete flux vacua. The conducting states are surface modes on the…
Numerical Hints for Dyon Condensation at $θ=2π$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Department of Physics, and Research and Education Center for Natural Sciences, Keio University（庆应义塾大学物理系及自然科学研究教育中心）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；Information Technology Center, The University of Tokyo（东京大学信息中心）；Department of Advanced Materials Science, The University of Tokyo（东京大学先进材料科学系）；Department of Information and Mathematical Sciences, Tokyo Woman’s Christian University（东京女子基督教大学信息数学科学系）；Department of Physics, Kyoto University（京都大学物理学系）
Topological excitations in the QCD vacuum take the form of coherent codimension one sheets with positive and negative sheets juxtaposed in a dipole layer. These sheets may be interpreted as Luscher's "Wilson bags," which are domain walls between discrete quasivacua labelled by a local value of the $θ$ parameter equal to $2πk$, with $k$ given by the number of units of background Ramond-Ramond flux. This picture of the vacuum is closely analogous to Coleman's description of the 2D massive Schwinger model, where $θ$ is interpreted as a background electric field, and a pointlike charged particle i…
We investigate SU(3) gauge theories in four dimensions with Nf fundamental fermions, on a lattice using the Wilson fermion. Clarifying the vacuum structure in terms of Polyakov loops in spatial directions and properties of temporal propagators using a new method "local analysis", we conjecture that the "conformal region" exists together with the confining region and the deconfining region in the phase structure parametrized by beta and K, both in the cases of the large Nf QCD within the conformal window (referred as Conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the …
