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We give a detailed analysis of the effects of scheme transformations in the vicinity of an exact or approximate infrared fixed point in an asymptotically free gauge theory with fermions.
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Instanton effects on β \beta were estimated in QCD in C. G. Callan, R. F. Dashen, and D. J. Gross, Phys. Rev. D 17
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G. ’t Hooft, in The Whys of Subnuclear Physics, Proc. 1977 Erice Summer School
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The latter is the case in QCD and technicolor theories: S. Weinberg, Phys. Rev. D 19
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E. Gardi, G. Grunberg and M. Karliner, JHEP 07
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For a chiral gauge theory with requisite fermion content, there is also the alternate possibility that the theory may confine and produce massless composite fermions, as discussed in G. ’t Hooft, Recent Developments in Gauge Theories, Cargése Summer Institute, 1979
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We focus here on an IR zero of the perturbative β \beta function. A nonperturbative zero in β \beta has been discussed in S. J. Brodsky, G. F. de Téramond, and A. Deur, Phys. Rev. D 81
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Z. Fodor et al., Phys. Lett. B 681
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For recent reviews of this and other gauge theories on the lattice, see talks in https://latt11.llnl.gov; http://lqcd.fnal.gov/(tilde)eneil/lat-exp-2011; and http://www.kmi.nagoya-u.ac.jp/workshop/SCGT12Mini
2011
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An analogous study of the effect of higher-loop terms in the β \beta function on the UV to IR evolution of a supersymmetric gauge theory has been carried out in T. A. Ryttov, R. Shrock, Phys. Rev. D 85
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W. Celmaster and R. J. Gonsalves, Phys. Rev. D 20
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S. J. Brodsky and X.-G. Wu, Phys.Rev. D 85
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