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Aspects of Chiral Symmetry

Abstract : 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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http://hal.in2p3.fr/in2p3-00084912
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Submitted on : Monday, July 10, 2006 - 10:26:48 PM
Last modification on : Wednesday, April 27, 2022 - 4:01:33 AM

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A. V. Smilga. Aspects of Chiral Symmetry. Advanced School in Quantum Chromodynamics, Jul 2000, Benasque, Spain. ⟨in2p3-00084912⟩

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