"Integrating in" and effective Lagrangian for non-supersymmetric Yang-Mills theory

Recently a non-supersymmetric analog of Veneziano-Yankielowicz (VY) effecti ve Lagrangian has been proposed and applied for the analysis of the theta d ependence in pure Yang-Mills theory. This effective Lagrangian is similar i n many respects to the VY construction and, in particular, exhibits a kind of low energy holomorphy which is absent in the full YM theory. Here we inc orporate a heavy fermion into this effective theory by using the "integrati ng in" technique. We find that, in terms of this extended theory, holomorph y of the effective Lagrangian for pure YM? theory naturally implies a holom orphic dependence on the heavy fermion mass. It is shown that this analysis fixes, under certain assumptions, a dimensionless parameter which enters t he effective Lagrangian and determines the number of non-degenerate vacuum sectors in pure YM theory. We also compare our results fbr the vacuum struc ture and theta dependence to those obtained recently by Witten on the basis of AdS/CFT correspondence. (C) 1999 Elsevier Science B.V.