  A field theoretic description of monopole condensation in strongly coupled
gauge theories is given by actions involving antisymmetric tensors B_{\mu\nu}
of rank 2. We rederive the corresponding action for 4d compact QED, summing
explicitly over all possible monopole configurations. Its gauge symmetries and
Ward identities are discussed. Then we consider the Wilsonian RGs for
Yang-Mills theories in the presence of collective fields (again tensors
B_{\mu\nu}) for the field strengths F_{\mu \nu} associated to the U(1)
subgroups. We show that a ``vector-like'' Ward identity for the Wilsonian
action involving B_{\mu\nu}, whose validity corresponds to monopole
condensation, constitutes a fixed point of the Wilsonian RG flow.
