Geodesic
Chirality-violating condensates in QCD and their connection with zero-mode solutions of quark Dirac equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 2, pp. 165-173

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We demonstrate that chirality-violating condensates in massless QCD arise entirely from zero-mode solutions of the Dirac equation in arbitrary gluon fields. We propose a model in which the zero-mode solutions are the ones for quarks moving in the instanton field and calculate the quark condensate magnetic susceptibilities $\chi$ of dimension three and $\kappa$ and $\xi$ of dimension five based on this model. The good correspondence of the values of $\chi$, $\kappa$, and $\xi$ obtained using this approach with the values found from the hadronic spectrum is a serious argument that instantons are the only source of chirality-violating condensates in QCD. We discuss the temperature dependence of the quark condensate and show that the phase transition corresponding to the temperature dependence $\alpha(T)$ of the quark condensate as an order parameter is a crossover-type transition.
Mots-clés : zero mode
Keywords: instanton, condensate. 
@article{TMF_2012_170_2_a0,
     author = {B. L. Ioffe},
     title = {Chirality-violating condensates in {QCD} and their connection with zero-mode solutions of quark {Dirac} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {165--173},
     publisher = {mathdoc},
     volume = {170},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_170_2_a0/}
}
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B. L. Ioffe. Chirality-violating condensates in QCD and their connection with zero-mode solutions of quark Dirac equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 2, pp. 165-173. http://geodesic.mathdoc.fr/item/TMF_2012_170_2_a0/