### Conveners

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

- Uwe-Jens Wiese (University of Bern, Switzerland)

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

- Waseem Kamleh (University of Adelaide)

$3+1$ dimensional QED with massless electrons is chirally symmetric, at least in the perturbative regime. This is true, even though this symmetry is anomalous, because QED lacks instantons. However, in the presence of external magnetic fields, approximate calculations based on Schwinger-Dyson equations indicate that chiral symmetry is spontaneously broken. In a constant external magnetic field...

Standard local updating algorithms experience a critical slowing down close to the continuum limit, which is particularly severe for topological observables. In practice, the Markov chain tends to remain trapped in a fixed topological sector. This problem further worsens at large $N$, and is known as $~\mathit{topological}$ $~\mathit{freezing}$.

To mitigate it, we adopt the parallel...

In order to understand the puzzle of the free energy of an individual quark in QCD, we explicitly construct ensembles with quark numbers $N_V\neq 0\!\mod 3$, corresponding to non-zero triality in a finite subvolume $V$ on the lattice. We first illustrate the basic idea in an effective Polyakov-loop theory for the heavy-dense limit of QCD, and then extend the construction to full Lattice QCD,...

Quark confinement is perhaps the most important emergent property of the theory of quantum chromodynamics. I review recent results studying centre vortices in SU(3) lattice gauge theory with dynamical quarks. Starting from the original Monte Carlo gauge fields, a vortex identification procedure yields vortex-removed and vortex-only backgrounds. The comparison between the original `untouched'...

We compute the topological susceptibility of $N_f = 2+1$ QCD at physical point in a temperature range going from 200 to 600 MeV. We adopt a multicanonical approach to enhance topological fluctuations and a definition of the susceptibility based on the spectral projectors over the eigenmodes of the staggered Dirac operator. This method allows to reduce lattice artifacts affecting the standard...

We investigate the isospin symmetry breaking effects in the two-flavour Schwinger model. Specifically, we check a prediction by Howard Georgi about automatic fine-tuning effects, i.e. that the isospin breaking is suppressed exponentially in the fermion mass $m_f$.

We study non-invertible defects constructed from dualities in the Cardy-Rabinovici model. The Cardy-Rabinovici model is a four-dimensional $U(1)$ lattice gauge theory with both electrically and magnetically charged particles, which is used as a playground for investigating the dynamics of the Yang-Mills theory with $\theta$ angle. A notable feature of this model is that the conjectured phase...

In this contribution, we report on our study of the properties of the Wilson flow and on the calculation of the topological susceptibility of $Sp(N_c=2N)$ gauge theories for $N=1,\cdots,4$.

The Wilson flow is shown to scale according to the quadratic Casimir operator of the gauge group, as was already observed for $SU(N_c)$, and the commonly used scales $t_0$ and $w_0$ are obtained

for a...

Charged particles in an Abelian Coulomb phase are non-local infra-particles that are surrounded by a cloud of soft photons which extends to infinity. Gauss' law prevents the existence of charged particles in a periodic volume. In a C-periodic volume, which is periodic up to charge conjugation, on the other hand, charged particles can exist. This includes vortices in the 3-d XY-model, magnetic...

We present our ongoing study of a set of solutions to the $SU(N)$ Yang-Mills equations of motion with fractional topological charge. The configurations are obtained numerically by minimising the action with gradient flow techniques on a torus of size $l^2\times\tilde{l}^2$ (with $\tilde{l}\equiv Nl$) and twisted boundary conditions. We pay special attention to the large $N$ limit, which is...