Monopole condensation and antisymmetric tensor fields: Compact QED and the Wilsonian RG flow in Yang-Mills theories Original Research Article

A field theoretic description of monopole condensation in strongly coupled gauge theories is given by actions involving antisymmetric tensors Bμν 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 Bμν) for the field strengths Fμνa associated to the U(1) subgroups. We show that a “vector-like” Ward identity for the Wilsonian action involving Bμν, whose validity corresponds to monopole condensation, constitutes a fixed point of the Wilsonian RG flow.