The Project

The standard model of elementary particle physics rests on gauge theories embodying symmetries. However, several elementary particles are not observable freely in nature. They are confined and only appear in bound states. Also not all symmetries are manifest, they are spontaneously broken. Hence the long-range structure is different from the short-range one.

The aim in this project is to study the realization of these cornerstone phenomena and investigate connections between them. The first focus is the interplay of how confinement and the Higgs-effect together shape the long-range structure of the theory. The second focus is how these effects generate the luminous mass in the universe. Of particular interest is, how confinement is involved. This involvement can only be indirect through the breaking of a symmetry, the chiral symmetry.

These investigations will provide a more solid understanding of fundamental non-perturbative phenomena in the standard model to be studied experimentally during the next years.

Scientific Project Details

The primary objective in this project is to understand the connection between confinement, and thus the structure of the physical state space, and spontaneously broken symmetries. These phenomena emerge in the non-perturbative interactions of Yang-Mills gauge-theories coupled to fermionic and scalar matter fields. The associated global symmetries are chiral symmetry and residual global gauge symmetries. To characterize and, if possible, isolate the relevant mechanisms and structures is the goal of this project. An important tool in this endeavor will be the possibility to restore and break global symmetries by phase transitions, e.\ g., at finite temperature.

In the case of the breaking of residual global gauge symmetries the main observables to be studied are the correlation functions for the elementary degrees of freedom. The gauge-dependent two-point functions encode the non-perturbative physics, while the three-point functions will given insight into how the dynamics is realized. To extract this information will be the main objective in this part of the project.

In case of chiral dynamics, recently found relations between the Polyakov loop as a quasi-order parameter for confinement and the spectrum of the Dirac operator, and thus chiral symmetry, will be exploited.

As the charge structure plays a significant role in the realization of confinement and its relation to global symmetries, two alternative charge structures for the matter fields will be explored. In one case the matter fields will be in the fundamental representation, in the other case in the adjoint representation.

In both cases, the situation in the confinement regime is rather similar for dynamical objects: The potential energy rises until string-breaking sets in. In case of fermionic fields, chiral symmetry is broken, while for scalars the global symmetry is unbroken. This can be changed to reach a deconfined phase, in which the status of the global symmetries is reversed: Chiral symmetry is restored, while global gauge symmetries become broken.

The goal of this project is to compare the different properties of the theories in the different phases, and to isolate underlying similarities. The comparison of fundamental and adjoint charges in both cases could show patterns leading to a more unified understanding of the different phenomena and their relations. To find these patterns is the ultimate aim of this project.

Secondary objectives are tied to this aim. This includes the understanding of how confinement is realized in the scalar-Yang-Mills system on the level of correlation functions, and how the chiral properties of adjoint charges differ from those of fundamental charges.

Further objectives are of technical nature, like an investigation of gauge-fixing effects on the scalar fields in lattice calculations.

Current Active Subprojects

• Fundamental and adjoint scalar propagators and vertices in Landau-gauge using lattice gauge theory and functional methods
• Topological properties of G2 Yang-Mills theory
• Chiral properties of adjoint fermions
• Scaling properties of Landau-gauge Green's functions
• Gauge-group dependence of Landau-gauge Green's functions
• Topology and Landau-gauge Green's functions
• Interpolating gauge Green's functions