Event

We describe a novel approach to gauge and generalized symmetries in QFT. It starts with the analysis of fundamental properties (additivity and Haag duality) that appear in the 'minimalistic' algebraic approach to QFT. We explain how different types of symmetries are associated with the violation of these properties in regions with different topologies. When such topologies are connected, we show how the violations of these properties generate abelian symmetry groups, and the algebra (commutation relations) is fixed. The generalized Dirac quantization condition then becomes the statement of causality in these QFT's. We then describe how the existence of order parameters with area law, like the Wilson loop for the confinement phase, implies the violation of these properties and the existence of more than one possible choice of algebras for the same theory. Natural ``entropic order parameters'' arise by this non-uniqueness. These entropic order parameters satisfy a "certainty principle" which quantitatively relates the physics of order (Wilson loops) and disorder parameters (t' Hooft loops). The certainty principle makes transparent the duality between constant and area law behaviors in symmetry breaking scenarios.