相关论文: ABCD and ODEs

I discuss some aspects of conformal defects and conformal interfaces in two spacetime dimensions. Special emphasis is placed on their role as spectrum-generating symmetries of classical string theory.

The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…

Characteristic integrals of Toda field theories associated to simple Lie algebras are presented in the most explicit forms, both in terms of the formulas and in terms of the proofs.

Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…

We discuss possible notions of conformal Lie algebras, paying particular attention to graded conformal Lie algebras with $d$-dimensional space isotropy: namely, those with a $\mathfrak{co}(d)$ subalgebra acting in a prescribed way on the…

We study quotients of quadratic forms and associated polar lines in the projective plane. Our results, applied pointwise to quadratic differential forms, shed some light on classical binary differential equations (BDEs) associated to…

We extend the work of [4] to support the conjecture that any conformal field theory with a large N expansion and a large gap in the spectrum of anomalous dimensions has a local bulk dual. We count to O(1/N^2) the solutions to the crossing…

Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line…

We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…

In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction…

The survey is devoted to algebraic structures related to integrable ODEs and evolution PDEs. A description of Lax representations is given in terms of vector space decomposition of loop algebras into a direct sum of Taylor series and a…

Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these…

Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…

We define vector fields, leaves and trajectories for schemes. With these tools, we are able to give a geometrical interpretation and to generalize several results of differential Galois theory and constructions on differential schemes. We…

The properties of completely degenerate fields in the Conformal Toda Field Theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy ordinary differential equation in…

Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments in the subject.

This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…

We develop a version of dipolar conformal field theory in a simply connected domain with the Dirichlet-Neumann boundary condition and central charge one. We prove that all correlation functions of the fields in the OPE family of Gaussian…

This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).