Dirac Eigenmodes and Center Vortices in SU(2) Lattice-QCD

01.08.2010 - 31.07.2013
Research funding project
The vortex model was first proposed as an explanation of quark confinement in Quantum Chromodynamics (QCD). Vortices are closed color magnetic flux lines, leading to narrowing of the color electric flux lines, a small gluonic flux tube - the gluon string, and therefore a linear potential between quarks and antiquarks. During the last years numericalresults showed that the vortex model is able to explain the strength of the gluonic flux tube, the string tension. Furthermore, the relevance of vortices for topological charge and chiral symmetry breaking was emphasised. In calculations of the topological charge on center vortex configurations we found a discrepancy with the so called index theorem. The index of a Dirac operator, i.e. the difference between positive and negative zero modes, is according to this theorem equal to the topological charge of a gauge configuration. However, some vortex configurations (spherical vortices) do not validate this theorem and the reason for that is still obscure. Furthermore we found special configurations with half-integer topological charge and their relevance and physical meaning is of great interest. To clarify these issues we plan to investigate different fermion representations, with regard to half-integer topological charge especially adjoint representations. Next to confinement, chiral symmetry breaking is the most important low-energy phenomenon in QCD, and a full understanding of this effect is of vital importance. For massless quarks the Lagrangian of QCD does not lead to an interaction of right- and left-handed quarks, of quarks with spins directed in and against the direction of momentum. This is the chiral symmetry of the QCD Lagrangian. The numerical investigations show that confinement is connected with a dynamical coupling of right and left-handed quarks, a dynamical breaking of chiral symmetry. This suggests that the topological excitations which are responsible for confinement are also the origin of the dynamical symmetry breaking. We plan to investigate if there are special structures in the gauge field which deflect quarks and lead to a dynamical coupling of right and left-handed quarks. Therefore we want to analyse the color structure of center vortices.

People

Project leader

Project personnel

Institute

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Research focus

  • Quantum Modeling and Simulation: 25%
  • Quantum many-body systems: 25%
  • Mathematical and Algorithmic Foundations: 25%
  • Modeling and Simulation: 25%

Keywords

GermanEnglish
chirale Symmetriebrechungchiral symmetry breaking
Dirac EigenzuständeDirac eigen modes
Zentrumsvorticescenter vortices
Farbeinschlussconfinement
QuantenchromodynamikQuantum chromo dynamics

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