Objective The project has two fundamental aims: A) Open new research horizons exploiting the interplay between Operator Algebras and Conformal Quantum Field Theory. B) Use Operator Algebraic methods for a deeper understanding of the internal structure of Conformal Quantum Field Theory, with a possible feedback for Operator Algebras. A) concerns two points in particular: - Find Noncommutative Geometrical structures associated with certain representations of Conformal Nets of von Neumann algebras and provide index theorems for quantum systems with infinitely many degrees of freedom in this framework. - Set up relations between Vertex Algebras and Local Conformal Nets and so provide new methods and results in each of these two subjects by importing and developing methods of the other subject. B) concerns in particular the analysis of following points, some motivated by A): - Structure and classification of conformal nets of von Neumann algebras on the circle and on two-dimensional spacetimes, and of their representations; in particular conformal supersymmetric models. - KMS and super-KMS functional structure in conformal models. - Boundary Conformal Field Theory, in particular regarding new thermalization effects. - Conformal subnet structure, in particular restrictions on the possible index values for conformal subnets. - Nuclearity and trace class properties for representations and modularity properties. Fields of science natural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebranatural sciencesmathematicsapplied mathematicsmathematical physicsconformal field theory Keywords Field Quantum Quantum Field Theory Theory Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2008-AdG See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA EU contribution € 1 044 750,00 Address VIA CRACOVIA 50 00133 Roma Italy See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Administrative Contact Giuseppe Novelli (Prof.) Principal investigator Roberto Longo (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA Italy EU contribution € 1 044 750,00 Address VIA CRACOVIA 50 00133 Roma See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Administrative Contact Giuseppe Novelli (Prof.) Principal investigator Roberto Longo (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
