Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-08-04
Phys.Lett. B364 (1995) 19-26
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, latex file, important changes in the non-abelian case. Some references added
Scientific paper
10.1016/0370-2693(95)01081-1
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 ${\tilde \tau}=-1/\tau$, $\tau=\frac{\theta}{2\pi}+\frac{4\pi i}{g^2}$.
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