  We investigate the gauge dynamics of nonsupersymmetric SU(N) gauge theories
featuring the simultaneous presence of fermionic matter transforming according
to two distinct representations of the underlying gauge group. We bound the
regions of flavors and colors which can yield a physical infrared fixed point.
As a consistency check we recover the previously investigated conformal windows
bounds when restricting to a single matter representation. The earlier
conformal windows can be imagined to be part now of the new conformal house. We
predict the nonperturbative anomalous dimensions at the infrared fixed points.
We further investigate the effects of adding mass terms to the condensates on
the conformal house chiral dynamics and construct the simplest instanton
induced effective Lagrangian terms.
