### Conveners

#### Vacuum Structure, Confinement, and Chiral Symmetry

- Jeff Greensite (San Francisco State University)

#### Vacuum Structure, Confinement, and Chiral Symmetry

- Waseem Kamleh (University of Adelaide)

#### Vacuum Structure, Confinement, and Chiral Symmetry

- Zhaofeng Liu (Institute of High Energy Physics)

#### Vacuum Structure, Confinement, and Chiral Symmetry

- Andreas Athenodorou (INFN - sez Pisa)
- Jon-Ivar Skullerud (National University of Ireland Maynooth)

We present results for $\eta$ and $\eta^\prime$ masses at the physical point.

The two independent decay constants, e.g., for the flavour singlet/non-singlet

basis, are also computed for both particles. The chiral and continuum limit extrapolation is performed on 21 CLS $n_f = 2+1$ Wilson Clover improved ensembles at four different lattice spacings and along two quark mass trajectories,...

We present results of gluonic and pseudoscalar matrix elements of the $\eta$ and $\eta'$ mesons at the physical quark mass point, in the continuum limit. The simulations are carried out on $n_f=2+1$ CLS ensembles, with non-perturbatively improved Wilson fermions. We discuss the renormalization of these quantities and check the consistency with the singlet and non-singlet axial Ward identities....

We measure the spatial distribution of all components of the color fields surrounding a static quark–antiquark pair in QCD with (2+1) HISQ flavors.

We isolate the nonperturbative component of the longitudinal chromoelectric

color field responsible for the linear term in the confining potential.

It has long been known that there is a phase transition between confined and unconfined phases of compact pure gauge QED on the lattice. In this work we report three manifestations of this phase change as seen in the Landau gauge photon propagator, the static potential, and distribution of Dirac Strings in the gauge fixed configurations. Each of these was calculated with large lattices with...

We present a major update on the spectrum of the closed flux-tube in $D=3+1$ $SU(N)$ gauge theories. Namely, we calculate the excitation spectrum of a confining flux-tube which winds around a spatial torus as a function of its length $l$, for short as well as long tubes. We do so for $N=3,5,6$ and two different values of the lattice spacing. Our states are characterised by the quantum numbers...

Pure gauge theories are rather different from theories with pure scalar and fermionic matter, especially in terms of the nature of excitations. For example, in scalar and fermionic theories, one can create ultra-local excitations. For a gauge theory, such excitations need to be closed loops that do not violate gauge invariance. In this talk, we present a study on the condensation phenomenon...

Confinement remains one the most interesting and challenging nonperturbative phenomenon in non-Abelian gauge theories. Recent semiclassical (for $SU(2)$) and lattice (for QCD) studies have suggested that confinement arises from interactions of statistical ensembles of instanton-dyons with the Polyakov loop. In this talk, I will present recent work which has extended the study of semiclassical...

We show that in the vicinity of the deconfinement transition the behaviour of the interquark potential in pure lattice gauge theories can be precisely predicted combining results from Conformal Field Theory, Effective String Theory and Integrable Models. We compare these predictions with simulations of the SU(2) gauge model both in (2+1) and in (3+1) dimensions.

When non-Abelian gauge fields in $SU(3)$ QCD have a line-singularity leading to non-commutability with respect to successive partial-derivative operations, the non-Abelian Bianchi identity is violated. The violation as an operator is shown to be equivalent to violation of the Abelian-like Bianchi identities. Then there appear eight Abelian-like conserved magnetic monopoles of the Dirac type in...

Lattice gauge scalar models allow analytical connection between confinement region and Higgs region for gauge invariant operators.

Combining the cluster expansion and the duality, we try to understand non-trivial contribution from scalar field in quark confinement mechanism.

In order to understand quark confinement further, moreover, we study double-winding Wilson loop averages in the...

We propose a subvolume method to study the $\theta$ 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 $\theta$...

Quark confinement mechanism is one of unsolved important problems in QCD. In the dual Meissner picture of color confinement, it is considered that the color flux tube between static quarks is caused by the condensation of color magnetic monopoles in the QCD vacuum. In this talk, we show new results of the dual Meissner effect due to the violation of non-Abelian Bianchi identity corresponding...

The dual superconductor picture is one of the most promising scenarios for quark confinement. To investigate this picture in a gauge-invariant manner, we have proposed a new formulation of Yang-Mills theory on the lattice, named the decomposition method, so that the so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. It was...

We review some highlights of the centre vortex research programme conducted by the CSSM in SU(3) lattice gauge theory. Starting from the original Monte Carlo gauge fields, a vortex identification procedure yields vortex-removed and vortex-only backgrounds. The original, vortex-removed, and vortex-only ensembles are compared by examining a number of different quantities. The removal of vortices...

This presentation examines the centre-vortex structure of Monte-Carlo generated gauge-field configurations using modern visualisation techniques. This time, the manner in which light dynamical fermion degrees of freedom impact the centre-vortex structure is explored. Focusing on the thin vortices identified by plaquettes having a non-trivial centre phase, the vortex structure is illustrated...

This presentation introduces new insights into the centre-vortex structure of lattice gauge fields, this time exploring the influence of dynamical fermions in the full-QCD vacuum. Calculations of both the Landau-gauge gluon propagator and the static quark potential reveal notable differences in the vortex phenomenology of pure-gauge and full-QCD simulations. Remarkably, configurations composed...

The important role of center vortices in dynamical chiral symmetry breaking and corresponding dynamical mass generation has been demonstrated in quenched studies of the Landau gauge quark propagator. We present the results of our investigation into the impact of center vortex removal on the Landau gauge quark propagator computed with overlap fermions on dynamical gauge fields. Upon removal of...

A novel method is proposed to determine the quark-diquark potential together with quark and diquark masses in the framework of Lattice Quantum Chromo Dynamics (LQCD). Treating a baryon as a quark-diquark bound state, we construct the corresponding two-body potential from the equal-time quark-diquark Nambu-Bethe-Salpeter (NBS) wave function by demanding it to satisfy the Schroedinger equation....

We study chirality of staggered quarks on the Dirac eigenvalue spectrum using deep learning techniques. The theory expects a characteristic pattern (we call it "leakage pattern") in the matrix elements of the chirality operator sandwiched between two eigenstates of staggered Dirac operator. Deep learning analysis gives 99.4(24)% accuracy per a single normal gauge configuration and 0.998 AUC...

We investigate the role of inhomogeneous field configurations in systems with a spontaneously broken continuous global symmetry. Textbooks tell us that the quantum effective potential of the system is flat in the thermodynamic limit. At the same time, spontaneous breaking is defined through the double limit, infinite volume at finite explicit breaking sources, which then approach zero. This...

Lattice QCD is a first principle tool that allows to solve the theory in the non-perturbative regime. The Landau gauge quark, gluon and ghost propagator have been recently computed using both large physical volumes to access the IR region and large gauge ensembles that reduce the corresponding statistical uncertainties. However, lattice QCD only offers a table of numbers and further treatment...

The lattice three-gluon vertex in the Landau gauge is revisited using a large physical volume $\sim(8\, \text{fm})^4$ and a large statistical ensemble. The improved calculation explores the symmetries of the hypercubic lattice to reduce the statistical uncertainties and to address the evaluation of the lattice artefacts. In particular we focus on the low energy behaviour of the vertex and...

We study the Landau-gauge quark-gluon vertex with 2 flavours of O(a) improved Wilson

fermions, for several lattice spacings and quark masses. In the limit of vanishing gluon momentum, we find that all nonzero form factors have a significant infrared strength, and that the leading form factor $\lambda_1$, multiplying the tree-level vertex structure, is significantly enhanced in the infrared...

We study analytic structures of the gluon, quark, and ghost propagators in the Landau-gauge QCD and general properties from the existence of unusual singularities. First, we investigate analytic structures of the QCD propagators using the massive Yang-Mills model, in which the one-loop gluon and ghost propagators are in good agreement with the numerical lattice results in the Landau gauge. We...

We report on the status of the analysis of the static potential in 2+1+1-flavor QCD. The static potential is obtained by measuring Wilson loops using the HISQ action, yielding the scales $r_{1}/a$, $r_{2}/a$, and the string tension $\sigma$. We put our emphasis on the possible effects due to the dynamic charm quark by comparing the lattice results to continuum results of the static potential...

In this talk I will present lattice results regarding the glueball

spectrum, the localization of Dirac eigenmodes and thermal monopoles

properties in trace-deformed YM theory. Trace deformation is an extra

piece added to the usual YM action, which stabilizes center symmetry

also in the limit of small compactification length. The study of

trace-deformation could give a deep insight on the...

We compare the behavior of the analytic instanton-dyon solutions to zero and near-zero-modes of the overlap Dirac operator measured on the finite temperature 2+1 flavor lattice QCD configurations, generated with domain wall fermion discreitzation. By performing numerical fit to the (near) zero-modes from lattice calculations, we extract information about the typical distance between the dyons...

The Schwinger model is often used as a testbed for conceptual and numerical

approaches in lattice field theory. Nevertheless, some of the rich physical

properties of the model in anisotropic volumes have not yet been tested.

For the multi-flavor finite temperature Schwinger model there is an

approximate solution by Hosotani et al. based on bosonization. We perform

thorough comparisons...

Topological terms contribute an imaginary part to the action such that for a numerical simulation of such systems the corresponding complex action problem has to be overcome. We address this task with newly developed density of states techniques combined with open boundary conditions that lift the integer quantization of the topological charge. We present results for U(1) and SU(2) lattice...

We reconstruct spectral functions from ghost and gluon propagators obtained through lattice QCD calculations with dynamical quarks. To this end, we employ Gaussian process regression (GPR) using kernel parametrizations that explicitly encode the analytically derived asymptotic scaling properties in the infrared and ultraviolet. The proposed ansatz allows us to consistently improve the...

Monopoles play crucial roles in the color confinement mechanism through condensing in the QCD vacuum, and the instantons induce spontaneous chiral symmetry breaking. Monopoles and instantons are closely related to each other and interact among quarks and gluons in the QCD vacuum. It is very interesting if we can show a clue to observe monopoles and instantons by experiments. Therefore, we...