We compute the chiral symmetries of the Lagrangian for confining
"vector-like" gauge theories with massless fermions in d-dimensional
Minkowski space and, under a few reasonable assumptions, determine the form of
the quadratic fermion condensates which arise through spontaneous breaking of
these symmetries. We find that for each type (complex, real, or pseudoreal) of
representation of the gauge group carried by the fermions, the chiral
symmetries of the Lagrangian, as well as the residual symmetries after
dynamical breaking, exactly follow the pattern of Bott periodicity as the
dimension changes. The consequences of this for the topological features of the
low-energy effective theory are considered.Comment: v2: Small additions and clarifications. To appear in Physics Letters