Celestial chiral algebras, colour-kinematics duality and integrability

Integrability, Duality and Strings †

After the two years ago work of Seiberg and Witten [1, 2], the Pandora box of string theory has been opened once more. The magic opening word has been duality. A web of exciting interrelated results it contains has appeared during the last months: string-string duality (U duality) [3]; the physical interpretation of the conifold singularity [4]; heterotic-type II dual pairs [3, 5, 6, 7, 8]; R-R...

Integrability and duality in two-dimensional QCD

We consider bosonized QCD2, and prove that after rewriting the theory in terms of gaugeinvariant fields, there exists an integrability condition that is valid for the quantum theory as well. Furthermore, performing a duality-type transformation we obtain an appropriate action for the description of the strong coupling limit, which is still integrable. We also prove that the model displays a com...

Duality and Operator Algebras

We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always weak *-continuous on dual operator spaces. For example , if X is a subspace of a C *-algebra A, and if a ∈ A satisfies aX ⊂ X and a * X ⊂ X, and if X i...

Distribution Algebras and Duality

Qcd, Chiral Random Matrix Theory and Integrability

1. Summary Random Matrix Theory has been a unifying approach in physics and mathematics. In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview of QCD, its low-energy limit and the microscopic limit of the Dirac spectrum which, as we will see in the second lecture, can be described by chir...