Elementary particles and their interactions are described by Quantum Field Theories (QFTs). Such theories usually exhibit a complex, non-perturbative vacuum structure and a rich phase diagram characteristic of macroscopic systems made of many, collectively interacting elementary particles at high temperature or density. In the goal to unravel the fundamental laws of physics that govern the interactions between elementary particles it is of central importance to understand the bulk properties of particle matter under these extreme conditions. Through the study of collective phenomena and macroscopic properties of particle matter one can reach new insight into the microscopic laws that control the interaction among elementary particles. In particular, this will allow to explore the crucial non-perturbative aspects of quantum field theories which are essential for the description of the physical vacuum structure and are difficult to access otherwise.

The most pronounced consequence of collective behaviour predicted by the Standard Model is the occurrence of phase transitions, which reflect the structure of quantum fields at different characteristic length scales. This is of utmost importance for our understanding of the properties of the Standard Model at low energies, i.e. its vacuum structure, as well as the early time evolution of hot matter in the early universe and the cold, dense matter accumulated in compact stars. Big Bang cosmology suggests that the universe evolved from an initial state of extreme (energy) density and temperature. An epoch of accelerated expansion (cosmological inflation) that ended by a violent outburst of particle creation was followed by the thermalization of the very early universe. During the following cooling process the hot and dense matter passed through a series of transitions which resulted in the breaking of various (approximate) global symmetries. These transitions were essential for generating the particle spectrum observed today in high energy experiments. Moreover, global features of the universe like the observed baryon number asymmetry or its large scale structure may be related to characteristic properties of these transitions.

Through an analysis of the non-perturbative structure of the vacuum and its modification at high temperatures and/or densities one will gain insight into the mechanisms behind important aspects of the Standard Model of elementary particle physics such as confinement of quarks and gluons, chiral symmetry breaking and the Higgs mechanism; it also allows to understand subtle topological aspects of QFTs which have far reaching cosmological consequences such as the tunneling between topologically distinct sectors of a QFT which may be closely related to the observed baryon number asymmetry of the universe.

A strong motivation for the intensive theoretical work which is performed worldwide on the phase structure of quantum field theories in general and the theory of strong interactions in particular lies in the fascination that in ultrarelativistic heavy ion collisions it may be possible to study experimentally the phase transitions in hot and dense matter as well as collective behaviour in an entirely new form of matter -- the quark gluon plasma. Very similar to the Big Bang, in those so-called Little Bangs a violent creation process of particles is followed by rapid thermalization and a phase transition from quark to hadronic matter. Understanding these experiments requires a solid understanding of the equilibrium thermodynamics of strongly interacting matter. Moreover, the specific conditions of these experiments give rise to new questions concerning the behaviour of hot and dense matter out of equilibrium and even far from equilibrium. This in turn is also of importance in the cosmological context for the discussion of e.g. transport processes.

Extreme temperatures and densities did not only exist in the early universe, but are also created in the early stages of supernovae explosions and exist in dense objects like neutron stars. A detailed knowledge of the properties of strongly interacting matter thus forms a basis for many considerations in astro-particle physics and cosmology and in particular provides a basis for the discussion of novel phenomena in the physics of dense matter such as the stability of quark stars, the existence of exotic matter or the appearance of colour superconducting phases.

In its research and educational program the IRTG puts emphasis on the field theoretic description of complex, non-perturbative phenomena occurring in the electroweak and strong sectors of the Standard Model as well as in beyond-the-standard-model theories. There will, however, be a strong focus on the physics of strongly interacting matter, which is described by Quantum Chromodynamics (QCD). Its non-perturbative structure is, in fact, particularly complicated due to the interplay of many non-perturbative effects that occur on different length scales. Understanding the interplay between these phenomena will also help to better control non-perturbative features of other QFTs, which are currently studied to construct a unified theory that could replace the Standard Model.

The IRTG brings together researchers which have complementary research experiences on a variety of aspects of complex, non-perturbative phenomena described by the Standard Model. Specific research topics are:

*Non-perturbative aspects of QCD: *

chiral and confining properties of the QCD vacuum; deconfinement and chiral symmetry restoration at high temperatures and densities; collective behaviour of elementary particle matter; phase transitions and critical phenomena

*Thermal field theory for phenomena in and out of equilibrium: *

equilibrium thermodynamics; resummation techniques at high temperature and density; effective field theories

*QCD phenomenology and relativistic heavy ion experiments: *

signatures for QGP formation; in-medium properties of hadrons; hard probes and deconfinement; thermalization, chemical and kinetic decoupling

*Cosmology: *

cosmological inflation; thermalization, chemical and kinetic decoupling in the early universe; phase transitions in the early universe and in compact stars; baryogenesis.

In principle one knows how to analyze the interactions among elementary particles in the vacuum as well as at high temperature by exploring the properties of the Euclidean path integral formulation of QFTs. However, most of the interesting properties of QFTs are of non-perturbative origin and cannot be explored with standard perturbative techniques which were developed to analyze their weakly coupled sector. In theoretical investigations of non-perturbative aspects numerical simulations of lattice regularized QFTs, resummed perturbative techniques as well as numerical and analytic renormalization group techniques play an important role. In all these approaches it has been realized that the systematic construction of effective theories, which focus on the physics on a particular length scale, largely facilitates the description of non-perturbative phenomena related to this scale.

It is a further feature of the IRTG that it brings together research groups working with a variety of state-of-the-art research techniques and tools, many of which have been pioneered by these groups and find worldwide application in Lattice Gauge Theory, (Thermal) Quantum Field Theory, Heavy Ion Physics and Cosmology. This includes

- numerical techniques for large scale lattice simulations on dedicated parallel computers to explore the non-perturbative structure of quantum field theories, including simulations of real-time and non-equilibrium processes
- advanced methods in quantum field theory, with strong emphasis on non-abelian gauge theories,
- resummation techniques which are partly based on the construction of a hierarchy of effective theories and are combined with variational techniques to incorporate non-perturbative features into perturbative expansions,
- numerical and analytic renormalization group techniques used to study universal properties and critical behaviour of quantum field theories.

It is the purpose of the IRTG to explore and further develop these modern field theoretic techniques and spread the know-how on these crucial field theoretic approaches among young graduate students in a dedicated educational program.