Nonperturbative results for two-index conformal windows

TL;DR

This paper derives nonperturbative insights into the conformal window of two-index theories using large and small $N_c$ relations, Schwinger-Dyson methods, and four-loop calculations, highlighting the unreliability of naive large $N_c$ extrapolations for small $N_c$.

Contribution

It introduces nonperturbative inequalities for the conformal window size applicable to any number of colors and relates the two-index conformal window to the adjoint case, supported by lattice results.

Findings

Naive large $N_c$ extrapolations are unreliable for $N_c<6.

The two-index conformal window is twice the size of the adjoint conformal window.

Lattice results for adjoint matter inform the dynamics of two-index theories.

Abstract

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.