### Conveners

#### Vacuum structure and confinement: A1a

- Manfried Faber (Vienna University of Technology)

#### Vacuum structure and confinement: A1b

- Dmitry Antonov (Petersburg Nuclear Physics Institute (PNPI))

#### Vacuum structure and confinement: A2a

- Jeff Greensite (San Francisco State University)

#### Vacuum structure and confinement: A2b

- Dmitry Antonov (Petersburg Nuclear Physics Institute (PNPI))

#### Vacuum structure and confinement: A3a

- Jeff Greensite (San Francisco State University)

#### Vacuum structure and confinement: A3b

- Dmitry Antonov (Petersburg Nuclear Physics Institute (PNPI))

#### Vacuum structure and confinement: A5a

- Manfried Faber (Vienna University of Technology)

#### Vacuum structure and confinement: A5b

- Jeff Greensite (San Francisco State University)

We report on a study of the Schwinger-Dyson equation (SDE) in the Euclidean formulation of local quantum gauge field theory, with Coulomb gauge condition $partial_i A_i = 0$. We compare the results of that study with a numerical simulation of lattice gauge theory and find that the infrared critical exponents and related quantities agree to within 1\% to 3\%. This raises the question, Why is...

The property of color confinement ("C-confinement"), meaning that all asymptotic particle states are color neutral, holds not only in QCD, but also in gauge-Higgs theories deep in the Higgs regime. In this talk I will describe a new and stronger confinement criterion, separation-of-charge confinement or "S-confinement," which is an extension of the Wilson area-law criterion to gauge + matter...

Confinement in QCD vacuum has been explained in terms of monopoles, and chiral symmetry breaking in terms of instantons. At finite temperature the latter get split to instanton-dyons and their semiclassical theory was shown to describe well both

Phase transitions. And yet, their interrelation to monopoles remained unclear.

In this talk it will be explained, in terms of the so called Poisson...

Conformal perturbation is a powerful tool to describe the behavior of statistical mechanics models and quantum field theories in the vicinity of a critical point. It was widely used in the past to describe two dimensional models and has been recently extended, thanks to the remarkable results of the bootstrap approach, also to three dimensional models. We show here that it can be also used to...

We discuss the dynamics and phases of a large class of chiral varieties of QCD. We find that the requirement of the correct realization of chiral symmetries in the infrared is sometimes so strong that it virtually determines the dynamics and phase of the system. In the models considered no gauge-invariant bi-fermion condensates exist, and yet in most cases the assumption of confinement and...

We study the recently discovered mixed discrete-chiral/center-symmetry (0-form/1-form) 't Hooft anomalies, which give new nontrivial consistency conditions that the IR dynamics of a strongly coupled QFT should obey. We use the simplest QFT example where such anomalies are present, the massless Schwinger model with charge-q fermions, to simply elucidate how they appear. We show that the...

Approaches to the sign problem based on the density of states have been recently revived by the introduction of the LLR algorithm, which allows us to compute the density of states itself with exponential error reduction. In this work, after a review of the generalities of the method, we show recent results for the Bose gas in four dimensions, focussing on the identification of possible...

During the last years it has become possible to address the nuclear liquid gas transition in QCD directly for

sufficiently heavy quarks, where combined strong coupling and hopping expansions are convergent. In this

contribution we study the Nc-dependence of the liquid gas transition and the equation of state of baryonic

matter. We find the transition to become more strongly first order with...

Z3 gauge theory mimics certain properties of QCD and might even have a quantitative link when the Z3 physical degrees of freedom are identified with the core of the so-called centre vortices of QCD. In particular, the Z3 theory confines static triality charges. In this talk, I will consider Z3 gauge theory with Z3 dynamical matter. A finite chemical potential is introduced to study this theory...

We investigate non-abelian Higgs theory in a constant strong magnetic field, where the lowest-Landau-level approximation can be used. At a critical magnetic value $eB=m^2$, the off-diagonal charged vector fields behave as one-dimensional massless fields and give a strong correlation along the magnetic direction, which may lead a new type of confinement caused by off-diagonal vector fields.

To establish the widely accepted dual superconductivity picture for explaining quark confinement, a reformulated version of $SU(N)$ Yang-Mills theory, which is based on the Cho-Faddeev-Niemi decomposition, has been recently developed. However, from a novel viewpoint, this decomposition is merely considered to be a nonlinear change of variables.

Within this framework, we consider a certain...

I discuss recent results on the relation between the localisation of low-lying Dirac eigenmodes, the restoration of chiral symmetry, and deconfinement in QCD and QCD-like models, providing evidence of a close connection between the three phenomena.

We perform a high precision measurement of the static quark-antiquark potential in three-dimensional SU(N) gauge theory with N=2 to 6. The results are compared to the effective string theory for the QCD flux tube and we obtain continuum limit results for the string tension and the non-universal leading order boundary coefficient, including an extensive analysis of all types of systematic...

We report about an ongoing lattice field theory project concerned with static hybrid mesons. In particular we study the structure of hybrid static potential flux tubes in Lattice Yang-Mills-theory by computing the square of the chromoelectric and chromomagnetic field strength components for several hybrid static potential quantum numbers. We find clear indications that the gluonic distribution...

I will review recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. The focus will be on the quark sector at finite temperatures. The temperature is introduced by compactifying a spatial dimension. The quark gap equation is solved numerically at finite temperatures. I will also report on preliminary studies of the effective potential of the Polyakov loop at 2-loop level.

QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified...

We discuss possible definitions of the Faddeev-Popov

matrix for the minimal linear covariant gauge on the

lattice and present preliminary results for the ghost

propagator.

The dynamical cancellation of the vacuum energy of the QCD sector in the infrared regime is a relevant problem for both particle physics and cosmology. We find an argument related to the existence of a Z_2-symmetry for the renormalization group flow derived from the bare Yang-Mills Lagrangian, and show that the cancellation of the vacuum energy may arise motivated both from the renormalization...

The existence of a mechanism with QCD to confine quarks and gluons to the interior of hadrons has long been accepted empirically. To explore the properties required for this confinement we present a field-strength description for a simple extended system of SU(2) charges with spherical symmetry and then impose confining boundary conditions on the time-independent Yang-Mills-Maxwell equations....

Recent developments of anomaly matching allows us to study the new nonperturbative aspects of various gauge theories. In this talk, I will show that there is a new 't Hooft anomaly for QCD with massless quarks containing the two-form gauge fields. This will give new constraints on the possible chiral symmetry breakings, and I will revisit the Stern phase (chiral symmetry broken phase without...

Ensembles of magnetic defects successfully explain many properties of confinement and are strongly believed to capture the (infrared) YM path-integral measure. In this work, we motivate and propose a measure to compute center element averages where vortices and chains (with non-Abelian d.o.f. and monopole fusion) are differentiated. When center vortices percolate and monopoles condense, using...

It has been conjectured that glueballs can be described by knot solitons in a low energy effective model of the Yang-Mills theory. In this talk, we consider knot solitons in the $F_2$ Skyrme-Faddeev-Niemi model, which can be interpreted as a low energy effective model of the $SU(3)$ Yang-Mills theory. It will be shown that the Euler-Lagrange equation reduces to that of the well-known $CP^1$...

A popular idea, originally proposed by 't Hooft, explains confinement in analogy to superconductivity in electromagnetism. Instead of the condensation of electrons, in QCD magnetic monopoles would condense leading to the confinement of the chromoelectric force. Since there are no elementary particles that could act as magnetic monopoles, the gluons themselves take on this role, which can be...

The Abelian dominance of the string tension for the fundamental sources in MA gauge was shown in the lattice simulations. However, it is known that, for higher representations, the naive "Abelian" Wilson loop, which is defined by using the diagonal part of the gauge field, does not reproduce the correct behavior. To solve this problem, for an arbitrary representation of an arbitrary gauge...

The dual superconductivity is a promising mechanism of quark confinement. In the preceding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice.

In this talk, we focus on the the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. By using our...

We consider the mass-deformed Yang-Mills theory in the Landau gauge which is obtained by just adding a gluon mass term to the Yang-Mills theory in the Landau gauge. We show that the decoupling solution is well reproduced by taking into account loop corrections from the mass-deformed Yang-Mills theory. Then we derive gluon confinement/deconfinement from the reflection-positivity...

Local formulations of quantum field theory provide a powerful framework in which non-perturbative aspects of QCD can be analysed. In this talk I will outline how this approach can be used to elucidate the general analytic features of QCD propagators.

In this talk, we consider SU(N) Yang-Mills theory quantized in the linear covari-

ant gauges, while taking into account the issue of Gribov copies. We construct the

one-loop e?ective potential for a set of mass dimension 2 condensates, including the

Gribov parameter, that re?ne the infrared region of the Gribov-Zwanziger theory,

whilst maintaining the renormalization group invariance.

This is...

Dyson--Schwinger equations are an established, powerful non-perturbative tool to investigate QCD. In the Hamiltonian formulation of a quantum field theory they allow variational calculations with non-Gaussian wave functionals: by means of DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the...

The covariant variational approach to Yang-Mills theory is further

developed. After reviewing the extension to finite temperature, we briefly

recall the effective action for the Polyakov loop and the critical

properties of the deconfinement phase transition within this approach.

The thermodynamics of pure Yang-Mills theory are studied in detail and

the resulting equation of state is compared...

In the Wilson's lattice formulation of QCD, a fermionic Fock space can be explicitly constructed at each time slice using canonical creation and annihilation operators. The partition function $\mathcal{Z}$ is then represented as the trace of the transfer matrix, which maps the Fock space at time $t$ in the one at time $t+1$. The usual functional representation of $\mathcal{Z}$ as a path...

Thermodynamics of the quark-gluon plasma at finite density is studied in the framework of the Field Correlator Method, where thermodynamical effects of Polyakov loops and the colormagnetic confinement force (CMC) is defined by the spatial Wilson loop projection are taken into account. It was shown that the CMC potential plays an important role in QGP thermodynamics providing the magnetic Debye...

We consider $SU(N)$ QCD in a new quadratic gauge which highlights certain characteristic of the theory in the non-perturbative sector. By considering natural hermiticity property of the ghost fields we cast this model as non-Hermtian but symmetric under combined Parity (P) and Time reversal (T) transformations. We explicitly study the PT phase transition in this model. This is very first...

We explain the essentials of the structure of the thermal ground state in the deconfining phase of SU(2) Quantum Yang-Mills theory. Applications here discussed involve the evolution of the coupling constant, aspects of the loop expansion of thermodynamical quantities and the polarization tensor the massless mode as well as a derivation of the 3D Ising critical exponent for the correlation...