Nonperturbative results for two-index conformal windows

Abstract: Via large and small Nc relations we derive nonperturbative results about the conformal window of two-index theories. Using Schwinger-Dyson methods as well as four-loops results we estimate subleading corrections and show that naive large number of colors extrapolations are unreliable when Nc is less than about six. Nevertheless useful nonper-turbative inequalities for the size of the conformal windows, for any number of colors, can be derived. By further observing that the adjoint conformal window is independent of the number of colors we argue, among other things, that: the large Nc two-index conformal window is twice the conformal window of the adjoint representation (which can be determined at small Nc) expressed in terms of Dirac fermions; lattice results for adjoint matter can be used to provide independent information on the conformal dynamics of two-index theories such as SU(Nc) with two and four symmetric Dirac flavors.