### Conveners

#### Section A

- Jeff Greensite (San Francisco State University)

#### Section A

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

#### Section A

- Manfried Faber (Vienna University of Technology)

#### Section A

- Jeff Greensite (San Francisco State University)

#### Section A

- Manfried Faber (Vienna University of Technology)

#### Section A

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

#### Section A

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

### Description

Section A: Vacuum Structure and Confinement

Mechanisms of quark confinement (vortices, monopoles, calorons...) and the structure of the vacuum in non-Abelian gauge theories. Chiral symmetry breaking, and the Dirac spectrum in the low-momentum region. Studies of ghost and gluon propagators. Confining strings and flux tubes, their effective actions. Renormalons and power corrections. Interface between perturbative and non-perturbative physics.

Conveners: D. Antonov (Heidelberg), M. Faber (TU Vienna), J. Greensite (San Francisco State U)

Focus Subsection: Emergent gauge fields and chiral fermions

Chiral Fermions and anomalous hydrodynamic effects in condensed matter systems, quantum simulators of QCD, topological phenomena in condensed matter systems.

Conveners: T. Schaefer (NC State U), V. Shevchenko (NRC Kurchatov I.)

X

I will review recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge at finite temperatures. The temperature is introduced by compactifying a spatial dimension. Results are presented for the chiral and dual quark condensate as well as for the Polyakov loop and the pressure

We discuss the phenomenon of (inverse) magnetic catalysis for both the deconfinement and chiral transition. We discriminate between the hard and soft wall model, which we suitably generalize to include a magnetic field. Our findings show a critical deconfinement temperature going down, in contrast with the chiral restoration temperature growing with increasing magnetic field. This is at odds...

Essential nonperturbative dynamical features of QCD are well captured in a semiclassical effective theory based on the extension of superconformal quantum mechanics to the light-front and its holographic embedding in a higher dimensional gravity theory. This new approach to hadron physics incorporates confinement, the appearance of a massless pion, and Regge spectroscopy consistent with...

Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties new gauge conditions are constructed to account for these gauge...

I will present recent progress in the calculation of nucleon resonances using the framework of Dyson-Schwinger and Bethe-Salpeter equations. The resulting mass spectra are obtained both from the three-body bound-state equation as well as its quark-diquark approximation starting from the level of QCD's propagators and vertices. I will outline how a better understanding of these n-point...

All the information about a quantum field theory is contained in the n-point functions. Once the n-point functions are computed they can be used in a next step to calculate hadron properties e.g. via the Bethe-Salpeter approach. On the level of three-point functions especially the three-gluon and quark-gluon vertices are of interest. The three-gluon vertex captures the property of...

Yang-Mills theory and 2-flavour QCD are investigated with the functional renormalisation group equation in the vacuum. Starting from the perturbative parameters of QCD as only input, the effective action is calculated in a vertex expansion. The focus is put on the properties of the corresponding 1PI correlations functions as well as the relation between confinement and chiral symmetry breaking.

Dyson-Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with wave functionals going beyond the Gaussian approximation. The various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms...

QCD thermodynamics in strong magnetic fields shows some unexpected features like inverse catalysis, which have been revealed mainly through lattice studies. Many effective descriptions, on the other hand, use Landau levels or approximate the system by just the lowest Landau level (LLL). Analyzing lattice configurations we ask whether such a picture is justified. We find the LLL to be separated...

We study $N_f=2$ lattice QCD with improved Wilson fermions at imaginary chemical potential $\mu_I.$ Simulations are made in the deconfinement phase at few values of $\mu_I/T$ to study Roberge-Weiss phase transitions at $\mu_I/T = \pm \pi/3$ and $\pi$. We measure spectrum of overlap Dirac operator in background of equilibrium configurations with variable $\mu_I/T$. Numerical evidence is...

We show how the increase in the Instanton-dyon density can explain both Confinement and Chiral symmetry breaking. We simulate an ensemble of 64 interacting Instanton-dyons for 2 colors and 0 or 2 quark flavors. We find that at low temperatures, the high density of dyons prefer a symmetric density, which leads to the confining value of the Polyakov Loop. At the same time the Chiral condensate...

The renormalization group procedure for effective particles (RGPEP) has been

developed during the last years as a non-perturbative tool for constructing

bound-states in quantum field theories [1]. It stems from the similarity

renormalization group procedure (SRG) [2] and introduces the concept of effective

particles, which differ from the point-like canonical, bare ones by

having a finite...

The confinement and the gribov ambiguity are two non-perturbative phenomena of great importance in QCD. Abelian dominance, a signature to the confinement, is mostly studied in Maximal abelian gauge which is Abelian projection. The Gribov ambiguity exists in various gauges. Algebraic gauges are more likely to be ambiguity free but are not compatible with the boundary conditions i.e.,the...

The properties of matter at finite baryon densities plays an

important role for the astrophysics of compact stars as well as for heavy

ion collisions or the description of nuclear matter. Because of the

sign problem of the quark determinant, lattice QCD cannot be

simulated by standard Monte Carlo at finite baryon densities.

I describe an alternative attempt to treat

dense QCD with an...

The LLR method was recently proposed for numerical computations of continuous density of states. The density of states approach is particularly useful when dealing with meta-stabilities and for computing free-energies. In this talk I will review the method and discuss compact U(1) Lattice Gauge Theory, for which our algorithm has proved to be highly efficient and provided results that...

Studies of QCD-like theories without a fermion sign problem at finite density by now have a rather long history already. I will report recent results from two-color QCD, with two instead of the usual three colors, and $G_2$-QCD, with gauge group $G_2$ instead of $SU(3)$. Both have bosonic diquark baryons. The physics of those is believed to be fairly well understood and qualitatively resembles...

We extract an effective Polyakov line action from an underlying SU(3) lattice gauge theory with dynamical fermions via the relative weights method. The center-symmetry breaking terms in the effective theory are fit to a form suggested by the hopping-parameter expansion, and the effective action is solved at finite chemical potential by a mean field approach. We show results for a small sample...

We extend the covariant variational approach for Yang-Mills theory

in Landau gauge to non-zero temperatures. The renormalization of the system

is revisited and it is shown how the zero-temperature counter terms can be

used to render the system finite at *any* temperature. Numerical solutions

for the thermal propagators are presented and compared to high-precision

lattice data. To...

This report is devoted to the study of the QCD phase diagram with nonzero chiral chemical

potential within lattice simulation. In particular, it is studied the question how nonzero

chiral chemical potential influences the transitions: confinement/deconfinement and

breaking/restoration of chiral symmetry. The results of the calculation can be

explained by the phenomenon which we called...

Studies of the QCD phase diagram at finite temperature and quark chemical potential are currently one of the most discussed topics in theoretical physics and are of great importance to better our understanding of heavy-ion collision experiments. However, there is considerable uncertainty about the detailed structure of the QCD phase diagram at high baryon densities. Models provide some insight...

We investigate Landau gauge $SU(3)$ Yang-Mills theory in a

systematic vertex expansion scheme for the effective action with

the functional renormalisation group.

Particular focus is put on the dynamical creation of the gluon mass

gap at non-perturbative momenta and the consistent treatment of

quadratic divergences. The non-perturbative ghost and transverse

gluon propagators as well as...

A massive expansion, based on *massive* free-particle propagators,

can be set up from first principles[1-3] and shown to be

a powerful variational tool disguised to look like a perturbative approximation[3].

By its optimization, the method provides an analytical tool for exploring the

propagators of QCD deep in the infrared of Minkowski space[3] and from first principles,

without having...

By breaking the initial SU(N) symmetry, we derive the Lagrangian[1] governing the dynamics of the massive scalar particles, which can be treated as the octet of the pseudoscalar mesons. The contribution of both the quark-gluon interaction and self-interaction gluon field into the masses of the octet particles is considered. Provided that the hadronization of the confinement matter into...

Strong magnetic backgrounds are known to modify QCD properties

at a non-perturbative level. We will discuss recent lattice results,

obtained for N_f = 2+1 QCD with physical quark masses, concerning

in particular the modifications and the anisotropies induced at the

level of the static quark-antiquark potential and of other confining

properties of strong interactions.

We discuss the confinement mechanism based on nonAbelian variety of dual superconductivity. Important hints come from physics of strongly-coupled infrared-fixed-point theories in N=2 supersymmetric QCD, which turn into confining vacua under a small relevant perturbation. The quest for the semiclassical origin of these nonAbelian monopoles, ubiquitous as the infrared degrees of freedom of...

We present the calculation of the next-to-leading order in the heavy quark-antiquark potentials within the framework of the effective string theory. Elaborate arguments for simplifying and reducing the number of dimensionful parameters of the effective string theory are also discussed.

Initially, we discuss a family of gauge fixing conditions that detect sectors of magnetic defects in continuum YM theories. The BRST symmetry cannot be globally defined, due to sector-dependent regularity conditions on the ghosts fields. This opens a window for the space of quantum states to be different from that implied when defects are removed. Next, we review how to integrate the partial...

- Introduction
- Conventional Higgs mechanism
- Higgs-Confinement: SU(2) case
- Higgs-Confinement: SU(3) case
- Conclusion and discussion

An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is briefly reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral $SU_{\rm L}(N_f)\times SU_{\rm R}(N_f)$ and $U_A(1)$ symmetries. Hadronization...

The QCD vacuum is populated by instantons that correspond to the tunneling processes in the vacuum. This mechanism creates the strong vacuum gluon fields. As result, The QCD vacuum instantons induce very strong interactions between light quarks, which was initiall almost massles. Such strong interactions bring about a large dynamical mass $M$ of the light quarks and can bound them to produce...

A new analytic non-perturbative, gauge invariant exact solution to QCD is derived. This solution is then compared with experimental data. Specifically high-energy proton-proton elastic scattering at ISR energies. A first proposal for LHC energies is examined also.

We discuss how the thermal ground state of an SU(2) Yang-Mills theory in its deconfining phase is composed of Harrington-Shepard (HS) (anti)calorons that are subject to deformation due to overlapping and static peripheries. The construction first performs a spatial coarse-graining over the central regions for HS (anti)calorons in isolation -- a unique process which determines the temperature...