We explore the consequences of imposing Polyakov's zig/zag invariance in th
e search for a confining string. We first find that the requirement of zig/
zag invariance seems to be incompatible with space-time supersymmetry. We t
hen try to find zig/zag-invariant string backgrounds on which to implement
the minimal-area prescription for the calculation of Wilson loops consideri
ng different possibilities. (C) 1999 Elsevier Science B.V.