S-Duality in Gauge Theories as a Canonical Transformation

We show that S-duality in four dimensional non-supersymmetric abelian gauge theories can be formulated as a canonical transformation in the phase space of the theory. This transformation is the usual interchange between electric and magnetic degrees of freedom. It is shown that in phase space the modular anomaly emerges as the result of integrating out the momenta degrees of freedom. The generalization to d dimensional abelian gauge theories of p forms is also considered. In the case of non-abelian gauge theories a careful analysis of the constraints implied by the canonical transformation shows that it does not relate Yang-Mills theories with inverted couplings. In fact the dual theory is shown to be of Freedman- Townsend's type, also with ${\tilde \tau}=-1/\tau$, $\tau=\frac{\theta}{2\pi}+\frac{4\pi i}{g^2}$.Comment: 13 pages, latex file, important changes in the non-abelian case. Some references adde

Duality and Canonical Transformations

We present a brief review on the canonical transformation description of some duality symmetries in string and gauge theories. In particular, we consider abelian and non-abelian T-dualities in closed and open string theories as well as S-duality in abelian and non-abelian non-supersymmetric gauge theories.Comment: 21 pgs, latex file, talk given at the Argonne Duality Institute, June 27-July 12, 1996, to appear in the e-proceeding