Conformality or confinement (II): One-flavor CFTs and mixed-representation QCD

Abstract

We study QCD-like four dimensional theories in the theoretically controlled framework of deformation theory and/or twisted partition function on S 1 × ℝ 3. By using duality, we show that a class of one-flavor theories exhibit new physical phenomena: discrete chiral symmetry breaking (χSB) induced by the condensation of topological disorder operators, and confinement and the generation of mass gap due to new non-selfdual topological excitations. In the ℝ 4 limit, we argue that the mass gap disappears, the χSB vacua are of runaway type, and the theory flows to a CFT. We also study mixed-representation theories and find abelian χSB by topological operators charged under abelian chiral symmetries. These are reminiscent to, but distinct, from Seiberg-Witten theory with matter, where 4d monopoles have non-abelian chiral charge. This examination also helps us refine our recent bounds on the conformal window. In an appendix, we also discuss mixed vectorlike/chiral representation theories, obtain bounds on their conformal windows, and compare with the all-order beta function results of arXiv:0911.0931. © 2009 SISSA.