  We argue that supersymmetric gluodynamics (theory of gluons and gluinos) has
a condensate-free phase. Unlike the standard phase, the discrete axial symmetry
of the Lagrangian is unbroken in this phase, and the gluino condensate does not
develop. Extra unconventional vacua are supersymmetric and are characterized by
the presence of (bosonic and fermionic) massless bound states. A set of
arguments in favor of the conjecture includes: (i) analysis of the effective
Lagrangian of the Veneziano-Yankielowicz type which we amend to properly
incorporate all symmetries of the model; (ii) consideration of an unsolved
problem with the Witten index; (iii) interpretation of a mismatch between the
strong-coupling and weak coupling instanton calculations of the gluino
condensate detected previously. Impact on Seiberg's results is briefly
discussed.
