  We use the worldline formalism to derive a universal relation for the lower
boundary of the conformal window in non-supersymmetric QCD-like theories. The
derivation relies on the convergence of the expansion of the fermionic
determinant in terms of Wilson loops. The expansion shares a similarity with
the lattice strong coupling expansion and the genus expansion in string theory.
Our result relates the lower boundary of the conformal window in theories with
different representations and different gauge groups. Finally, we use SQCD to
estimate the boundary of the conformal window in QCD-like theories and compare
it with other approaches.
