Operator Algebras and Conformal Field Theory

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.

Field of science

• /natural sciences/mathematics/pure mathematics/algebra
• /natural sciences/physical sciences/quantum physics/quantum field 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

Host institution

Beneficiaries (1)