PHASES OF ANTISYMMETRIC TENSOR FIELD-THEORIES

We study the different phases of field theories of compact antisymmetr ic tensors of rank h - 1 in arbitrary space-time dimensions D = d + 1. Starting in a 'Coulomb' phase, topological defects of dimension d - h - 1 ((d - h - 1)-branes) may condense leading to a generalized 'confi nement' phase. If the dual theory is also compact the model may also h ave a third, generalized 'Higgs' phase, driven by the condensation of the dual (h - 2)-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low-energy effective acti on for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the C oulomb phase but massive for the Higgs and confinement phases. We illu strate our prescription in detail for compact QED in 4D, Compact QED a nd O(2) models in 3D, as well as a periodic scalar field in 2D (string s on a circle), are also discussed. In this last case we show how T-du ality is maintained if one considers both world-sheet instantons and t heir duals. We also unify various approaches to the problem of the axi on mass in 4D string models. Finally we discuss possible implications of our results for non-perturbative issues in string theory. (C) 1997 Elsevier Science B.V.