Related papers: Quantum Langlands duality and conformal field theo…

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…

We formulate a two-parameter generalization of the geometric Langlands correspondence, which we prove for all simply-laced Lie algebras. It identifies the q-conformal blocks of the quantum affine algebra and the deformed W-algebra…

Following the formuation of Borcherds, we develop the theory of (quantum) vertex algebras, including several concrete examples. We also investigate the relationship between the vertex algebra and the chiral algebra due to Beilinson and…

In our paper arXiv:1701.03146 we established, for every simply-laced Lie algebra g, a canonical isomorphism between the spaces of deformed conformal blocks of the deformed W-algebra and the quantum affine algebra corresponding to g, which…

A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…

We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in…

We discuss the analogy between collapsing Conformal Field Theories and measured Gromov-Hausdorff limit of Riemannian manifolds with non-negative Ricci curvature. Motivated by this analogy we propose the notion of non-commutative…

A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.

Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.

Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…

We show that the numerical local Langlands duality for GL_n and the T - duality of two-dimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its l-adic and…

This is the author's PhD thesis, which focuses on the so-called Landau-Ginzburg/conformal field theory correspondence. This correspondence dates from the late 80s and early 90s in the physics literature and in particular, it predicts a…

Firstly we discuss different versions of noncommutative space-time and corresponding appearance of quantum space-time groups. Further we consider the relation between quantum deformations of relativistic symmetries and so-called doubly…

We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the…

In this brief review we introduce the Landau-Ginzburg/conformal field theory correspondence, a result from the physics literature of the late 80s and early 90s which predicts a relation between categories of matrix factorizations and…

Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…

Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…

We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results.

Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally…

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…