Recent efforts in lattice evaluation of the topological susceptibility had shown that at high temperatures it is given by well-separated instantons (even in QCD with light fermions, where those are highly suppressed). Recent development of the semiclassical theory suggest that below $T_{max}\sim 2.5T_c$, where Polyakov line has values between one and zero, the topology ensemble can be represented by a plasma of instanton constituents (called instanton-dyons or instanton-monopoles). It has been shown that such ensemble undergoes deconfinement and chiral transitions, semi-qualitatively reproducing the lattice results. There are ongoing efforts to locate them on the lattice, or use (flavor-dependent) periodicity phases of the deformed versions of QCD on the lattice and semiclassically, in order to test this theory. We here propose another possibly useful tool: the topological susceptibility of a sub-lattice.
Theories of interacting gauge fields and fermions can possess a running gauge coupling with an infrared attractive fixed point (IRFP). We present a minimal description of the physics of these systems and comment on some simple expectations for results from lattice simulations done within the basin of attraction of the IRFP in these theories.
Laplacian gauge fixing was introduced to find a unique representative of the gauge orbit, which on the lattice could be implemented by a ``finite'' algorithm. What was still lacking was a perturbative formulation of this gauge, which will be presented here. However, renormalizability is still to be demonstrated. For torodial and spherical geometries a detailed comparison with the Landau (or Coulomb) gauge will be made.
We analyze SU(2) gauge theory in a constant chromomagnetic field in three dimensions. Our analysis instead of supporting the existence of a non-trivial minimum in the effective potential, corroborates the evidence of the unstable modes on the lattice.
The topology conserving gauge action proposed by Luescher is expected to reduce the number of non-smooth gauge configurations as well as the topology change compared to the conventional actions for the same lattice spacings. We report our quenched QCD study of the topological stability and the scaling violation of the static quark potential. We find that the the topology change is indeed suppressed when the parameter epsilon is of order one. We also find that the scaling violation in the static quark potential remain reasonably small in the parameter range of our study. Our study is done at th…
The topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills Theory. For this purpose the continuum analog of the maximum center gauge is constructed.
We apply the topology conserving gauge action proposed by Luescher to the four-dimensional lattice QCD simulation in the quenched approximation. With this gauge action the topological charge is stabilized along the hybrid Monte Carlo updates compared to the standard Wilson gauge action. The quark potential and renormalized coupling constant are in good agreement with the results obtained with the Wilson gauge action. We also investigate the low-lying eigenvalue distribution of the hermitian Wilson-Dirac operator, which is relevant for the construction of the overlap-Dirac operator.
Topologically non-trivial gauge field configurations are an interesting aspect of non-abelian gauge theories. These become particularly important upon quantizing the theory, especially through their effect on the pseudo-scalar spectrum. These effects are closely tied to chiral anomalies and the possibility of CP violation in the strong interactions.
We investigate the distribution of low-lying eigenmodes of hermitian Wilson-Dirac operator, $H_W$, with the gauge action whose form is designed to avoid topology change, as well as with the standard plaquette action. On the quenched lattices, the former gauge action exhibits less density of low-lying eigenmodes of $H_W$ compared to the latter at the same lattice spacing. We also show preliminary results for the dynamical simulation with two flavors of overlap fermions.
Momentum space topology of relativistic gauge theory is considered. The topological invariants in momentum space are introduced for the case, when there is the mass gap while the fermion Green functions admit zeros. The index theorem is formulated that relates the number of massless particles and generalized unparticles at the phase transitions to the jumps of the topological invariants. The pattern is illustrated by the lattice model with overlap fermions.
The axial anomaly in abelian lattice gauge theories is shown to be equal to a simple quadratic expression in the gauge field tensor plus a removable divergence term if the lattice Dirac operator satisfies the Ginsparg-Wilson relation. The theorem is a consequence of the locality, the gauge invariance and the topological nature of the anomaly and does not refer to any other properties of the lattice theory.
Based on a large number of smearing steps, we classify SU(3) gauge field configurations in different topological sectors. For each sector we compare the exact analytical predictions for the microscopic Dirac operator spectrum of quenched staggered fermions. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero, showing explicitly that the smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are insensitive to gauge field topology. On the smeared configurations, $4ν$ eigenvalues clearly separate out …
We investigate the locality property of the overlap-Dirac operator on gauge configurations generated with extra Wilson fermions. By such extra terms we expect that the structure of the Aoki phase would change drastically. In particular, we study the possibility of defining the overlap-Dirac operator in the strong coupling regime keeping its exponential locality.
We test a set of lattice gauge actions for QCD that suppress small plaquette values and in this way also suppress transitions between topological sectors. This is well suited for simulations in the epsilon-regime and it is expected to help in numerical simulations with dynamical quarks.
Lin and Liu evaluate the nucleon expectation value of the non gauge-invariant canonical quark momentum operator on a lattice, and obtain zero. They conclude that my argument that, despite the non gauge-invariance of the operator, its physical matrix elements \emph{are} gauge-invariant, cannot be correct. I show that their result has no bearing on the question of gauge-invariance, and also point to an amusing lattice paradox.
The interplay between between gauge-field winding numbers, theta-vacua, and the Dirac operator spectrum in finite-volume gauge theories is reconsidered. To assess the weight of each topological sector, we compare the mass-dependent chiral condensate in gauge field sectors of fixed topological index with the answer obtained by summing over the topological charge. Also the microscopic Dirac operator spectrum in the full finite-volume Yang-Mills theory is obtained in this way, by summing over all topological sectors with the appropriate weight.
In this work we study the topological properties of the $G_2$ lattice gauge theory by means of Monte Carlo simulations. We focus on the behaviour of topological quantities across the deconfinement transition and investigate observables related to the $θ$ dependence of the free energy. As in $SU(N)$ gauge theories, an abrupt change happens at deconfinement and an instanton gas behaviour rapidly sets in for $T>T_c$.
It is argued by the author that the canonical form of the quark energy-momentum tensor with a partial derivative instead of the covariant derivative is the correct definition for the quark momentum and angular momentum fraction of the nucleon in covariant quantization. Although it is not manifestly gauge invariant, its matrix elements in the nucleon will be non-vanishing and are gauge invariant. We test this idea in the path-integral quantization by calculating correlation functions on the lattice with a gauge-invariant nucleon interpolation field and replacing the gauge link in the quark latt…
We investigate SU(2) gauge fields topology using new approach, which exploits the well known connection between SU(2) gauge theory and quaternionic projective sigma-models and allows to formulate the topological charge density entirely in terms of sigma-model fields. The method is studied in details and for thermalized vacuum configurations is shown to be compatible with overlap-based definition. We confirm that the topological charge is distributed in localized four dimensional regions which, however, are not compatible with instantons. Topological density bulk distribution is investigated at…
Z2 Lattice Gauge Theory on Non-trivial Topology and Its Quantum Simulation
Tsinghua University（清华大学）；Fudan University（复旦大学）；Southern University of Science and Technology（南方科技大学）；International Quantum Academy, Shenzhen（深圳国际量子研究院）；Shanghai Institute for Advanced Studies, University of Science and Technology of China（中国科学院上海高等研究院）
Recently, Hoshina, Fujii, and Kikukawa pointed out that the naive lattice gauge theory action in Minkowski signature does not result in a unitary theory in the continuum limit, and Kanwar and Wagman proposed alternative lattice actions to the Wilson action without divergences. We here show that the subtlety can be understood from the asymptotic expansion of the modified Bessel function, which has been discussed for path integral of compact variables in nonrelativistic quantum mechanics. The essential ingredient for defining the appropriate continuum theory is the $i\varepsilon$ prescription, a…
Recently Appelquist, Terning, and Wijewardhana investigated the zero temperature chiral phase transition in SU(N) gauge theory as the number of fermions N_f is varied. They argued that there is a critical number of fermions N^c_f, above which there is no chiral symmetry breaking and below which chiral symmetry breaking and confinement set in. They further argued that that the transition is not second order even though the order parameter for chiral symmetry breaking vanishes continuously as N_f approaches N^c_f on the broken side. In this note I propose a simple physical picture for the spectr…
We discuss the dependence of pure Yang-Mills equation of state on the choice of gauge algebra. In the confined phase, we generalize to an arbitrary simple gauge algebra Meyer's proposal of modelling the Yang-Mills matter by an ideal glueball gas in which the high-lying glueball spectrum is approximated by a Hagedorn spectrum of closed-bosonic-string type. Such a formalism is undefined above the Hagedorn temperature, corresponding to the phase transition toward a deconfined state of matter in which gluons are the relevant degrees of freedom. Under the assumption that the adjoint string tension …
We revisit the issue of defining the entropy of a spatial region in a broad class of quantum theories. In theories with explicit regularizations, working within an elementary but general algebraic framework applicable to matter and gauge theories alike, we give precise path integral expressions for three known types of entanglement entropy that we call full, distillable, and gauge-invariant. For a class of gauge theories that do not necessarily have a regularization in our framework, including Chern-Simons theory, we describe a related approach to defining entropies based on locally extending …
