Anomalous Interactions of Five Dimensional USp(2k) Gauge Theory

We consider the five dimensional $USp(2k)$ gauge theory which consists of one antisymmetric and $n_f$ fundamental hypermultiplets. This gauge theory is a many-probe generalization of the SU(2) gauge theory in five dimensions considered by Seiberg in the context of probing type I superstring by a D4-brane. This gauge theory can also be obtained from the USp(2k) matrix model by matrix T-dual transformations in the large k limit. We exhibit the anomalous interaction associated with this five dimensional theory on the new phase, where the vacuum expectation values (vevs) of the scalars belonging to the antisymmetric hypermultiplet are also nonvanishing. On the Coulomb phase, the anomalous interaction has been computed in [1, 2].