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Chirality-violating condensates in QCD and their connection with zero-mode solutions of quark dirac equations

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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 χ of dimension three and κ and ξ of dimension five based on this model. The good correspondence of the values of χ, κ, and ξ 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 α(T) of the quark condensate as an order parameter is a crossover-type transition.

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Authors and Affiliations

  1. Institute of Theoretical and Experimental Physics, Moscow, Russia

    B. L. Ioffe

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  1. B. L. Ioffe
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Correspondence to B. L. Ioffe.

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Dedicated to the memory of Albert Nikiforovich Tavkhelidze, my friend, an outstanding physicist, and a great organizer of science in the USSR and Russia.

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 170, No. 2, pp. 165–173, February, 2012.

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Ioffe, B.L. Chirality-violating condensates in QCD and their connection with zero-mode solutions of quark dirac equations. Theor Math Phys 170, 132–138 (2012). https://doi.org/10.1007/s11232-012-0015-8

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