Conformality or confinement: (IR)relevance of topological excitations

Abstract

We study aspects of the conformality to confinement transition for non-supersymmetric Yang-Mills theories with fermions in arbitrary chiral or vectorlike representations. We use the presence or absence of mass gap for gauge fluctuations as an identifier of the infrared behavior. Present-day understanding does not allow the mass gap for gauge fluctuations to be computed on R*4. However, recent progress allows its non-perturbative computation on R*3xS*1 by using either the twisted partition function or deformation theory, for a range of S*1 sizes depending on the theory. For small number of fermions, Nf, we show that the mass gap increases with increasing radius, due to the non-dilution of monopoles and bions, the topological excitations relevant for confinement on R*3xS*1. For sufficiently large Nf, we show that the mass gap decreases with increasing radius. In a class of theories, we claim that the decompactification limit can be taken while remaining within the region of validity of semi-classical techniques, giving the first examples of semiclassically solvable Yang-Mills theories at any size S*1. For general non-supersymmetric vectorlike or chiral theories, we conjecture that the change in the behavior of the mass gap on R*3xS*1 as a function of the radius occurs near the lower boundary of the conformal window and give non-perturbative estimates of its value. For vectorlike theories, we compare our estimates of the conformal window with existing lattice results, truncations of the Schwinger-Dyson equations, NSVZ beta function-inspired estimates, and degree of freedom counting criteria. For multi-generation chiral gauge theories, to the best of our knowledge, our estimates of the conformal window are the only known ones.

40 pages, 3 figures; modified various comments, reference added

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