Nonperturbative results for two-index conformal windows

Understand

Via large and small $N_c$ 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 $N_c$ is less than about six.
• Nevertheless useful nonperturbative 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 $N_c$ two-index conformal window is twice the conformal window of the adjoint representation (which can be determined at small $N_c$) 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($N_c$) with two and four symmetric Dirac flavors.