We uncover novel solutions of the 't Hooft anomaly matching conditions for
scalarless gauge theories with matter transforming according to higher
dimensional representations of the underlying gauge group. We argue that, if
the duals exist, they are gauge theories with fermions transforming according
to the defining representation of the dual gauge group. The resulting conformal
windows match the one stemming from the all-orders beta function results when
taking the anomalous dimension of the fermion mass to be unity which are also
very close to the ones obtained using the Schwinger-Dyson approximation. We use
the solutions to gain useful insight on the conformal window of the associated
electric theory. A consistent picture emerges corroborating previous results
obtained via different analytic methods and in agreement with first principle
lattice explorations.Comment: RevTeX, 23 pages, 3 figure
