EXACT ZERO-MOMENTUM SUM-RULES IN D=3 GAUGE-THEORY

We derive, for non-abelian pure gauge theory, an infinite set of sum rules for connected zero-momentum matrix elements of the condensate operator SIGMA(G(ij)a)2(x) in d = 3; these are equivalent to an effective action for this operator. These sum rules are analogous to similar ones derived, at the one-loop level, for d = 4 gauge theory and predict a non-zero positive value of [G(ij)2] and a negative vacuum energy. Some applications to effective glueball couplings and approximations to the evaluation of [G(ij)2] are discussed.