Any compact group is a gauge group

The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive element k of G, and a complete normal algebra of fields carrying the localizable charges, on which k defines the Bose/Fermi grading. We show here that any such pair {G,k}, where G is compact metrizable, does actually appear. The corresponding model can be chosen to fulfill also the split property. This is not a dynamical phenomenon: a given {G,k} arises as the gauge group of a model where the local algebras of observables are a suitable subnet of local algebras of a possibly infinite product of free field theories.Comment: 13 pages, LaTeX. To appear on Reviews in Mathematical Physics. References added; minor changes in styl

Duality, Strings and Supergravity: a Status Report

We will report on recent advances in the understanding of non-perturbative interconnections between different string dualities. Weak-strong coupling duality (S-duality) and T-duality (symmetry under compactification on dual tori) allows one to compare and explore the strong coupling regime of seemingly unrelated theories. These theories naturally merge in a quantum version of supergravity called M-theory. The dynamical role of `branes' of different nature and the new dynamical tool of (M)atrix formulation of M-theory will be briefly mentioned.Comment: 12 pages, LaTeX; Plenary Talk given at the XII International Congress of Mathematical Physics, 13-19 July 1997, Brisbane, Australi

Spacetime and Fields, a Quantum Texture

We report on joint work, past and in progress, with K.Fredenhagen and with J.E,Roberts, on the quantum structure of spacetime in the small which is dictated by the principles of Quantum Mechanics and of General Relativity; we comment on how these principles point to a deep link between coordinates and fields. This is an expanded version of a lecture delivered at the 37th Karpacz School in Theoretical Physics, February 2001.Comment: LaTeX, 15 pages. Misprints and wording corrected, references added; change in section 3. Related references: hep-th/0303037, hep-th/0201222, hep-th/030110