Aspects of Chiral Symmetry

Details Aspects of Chiral Symmetry Aspects of Chiral Symmetry

2000-10-06

arxiv.org/abs/hep-ph/0010049v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

Based on the lectures given at the Advanced School in Quantum Chromodynamics (Benasque, July 2000). To be published in the Fes

Scientific paper

We give a pedagogical review of implications of chiral symmetry in QCD. First, we briefly discuss classical textbook subjects such as the axial anomaly, spontaneous breaking of the flavor-nonsinglet chiral symmetry, formation of light pseudo-Goldstone particles, and their effective interactions. Then we proceed to other issues. We explain in some detail a recent discovery how to circumvent the Nielsen--Ninomiya's theorem and implement chirally symmetric fermions on the lattice. We touch upon such classical issues as the Vafa-Witten's theorem and 't Hooft's anomaly matching conditions. We derive a set of exact theorems concerning the dynamics of the theory in a finite Euclidean volume and the behavior of the Dirac spectral density. Finally, we discuss an imaginary world with a nonzero value of the vacuum angle theta.

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