The hadronic string: Properties and mechanism of formation

To the best of our knowledge, the fundamental building blocks of matter are quarks and leptons. While leptons have been found free in nature, single free quarks have not been observed. They always occur bound either in triplets (baryons) or as quark-antiquark pairs (mesons). This is known as the problem of quark confinement. It is generally believed, and in certain cases checked, that the quantum field theory of quarks and gluons (QCD - Quantum Chromodynamics) describes this confining interaction. The energy range where QCD has been verified in experiment is the region where the interactions between the quarks is weak. This energy regime can be handled by the perturbative formulation of QCD. However this formulation does not tell us why free quarks are never seen. The only non-perturbative approach which has the potential to do this is a space-time discretized version called Lattice QCD. It is possible to do non-perturbative studies in Lattice QCD by doing simulations on powerful computers. While these studies show that indeed in our everyday energy regime free quarks cannot occur, it does not explain the underlying mechanism of quark confinement. One of the most appealing scenarios of confinement is that in QCD, flux tubes or strings are formed between the quarks holding them together in a bound state. It is believed that topologically non-trivial configurations which dynamically generated in the vacuum are responsible for formation of the string. These configurations can be looked at from the geometric (defined in terms of the field strength) or algebraic (defined through the Dirac operator) point of view. In this project we propose to study properties of the string and the mechanism behind its formation. Using new and precise algorithms as well as improved operators we hope to address this issue both from the algebraic and geometric point of view. On the lattice, since there is no notion of continuum topology, it is essential to check that both approaches give physically equivalent results.