Conformal  Field Theory and Related Topics

Timetable

Abstracts and Tranparencies of Talks:

Pasquale Calabrese  Transparencies (pdf)

Entanglement Entropy and Quantum Field Theory

Anastasia Doikou  Transparencies (pdf)

On integrable quantum spin chains with open boundaries

We review how c-number solutions of the reflection equation arise
by implementing appropriate representations of the affine Hecke algebra.
Having specified such solutions we construct the corresponding
open spin chain, and we also study its exact symmetry. In particular,
we derive boundary non-local charges, which turn out to be conserved
quantities, that is they commute with the transfer matrix of the
open spin chain.

Benjamin Doyon  Transparencies (pdf)

A new viewpoint on form factors and correlation functions in the Ising field theory at finite temperature

I will identify a concept of "finite-temperature form factor" that appears naturally when considering correlation functions in the (massive) Ising field theory at finite temperature. This concept is slightly different from that involved in previous studies of finite-temperature correlation functions. I will explain how such "form factors" provide large-distance expansions of finite-temperature correlation functions, how to evaluate some of them from their analytical properties, and how they can be used to calculate form factors on the cylinder.

Misha Feigin  Transparencies (pdf)

Generalized Calogero-Moser-Sutherland systems

We consider generalized quantum Calogero-Moser-Sutherland operator with trigonometric potential when the singularity hyperplanes form not necessarily fully symmetric configuration. The operators under consideration have full set of quantum integrals. At integer coupling parameters the Baker-Akhiezer function (joint singular eigenfunction) has closed expression. It satisfies a family of difference equations in the spectral parameters of Ruijsenaars-Macdonald rational type, these difference operators also commute. The results were obtained in the works of Chalykh, Veselov, and the author. 

Guenter von Gehlen  Transparencies (pdf)

A large class of chiral 3D integrable lattice spin models

We consider integrable models defined on a 3-dimensional oriented cubic lattice. The dynamical variables are taken to be elements of an ultra-local Weyl algebra atroot of unity attached to the links of the lattice. The basic object   is the Sergeev invertible canonical operator R which maps the Weyl variables on the three ingoing links of a lattice vertex to the three Weyl variables on the outgoing links. Sergeev has postulated a linear problem involving the Weyl variables which, together with a Baxter Z-invariance, determines R uniquely. A simple argument shows that this R satisfies the tetrahedron equation. A tedious verification of the tetrahedron equation is avoided. Working at N-th root of unity, a N x N-matrix representation for the Weyl elements is taken and R decomposes into a functional mapping of the Weyl centers and a matrix conjugation. The matrix conjugation operator satisfies a modified tetrahedron equation with "rapidities" determined by the functional transformation. The latter is a discrete classical integrable system of trilinear Hirota form which can be solved by standard methods of algebraic geometry. The Zamolodchikov-Bazhanov-Baxter model arises when chosing the trivial solution to the classical system. Due to the flexibility of the 3D parametrization, interesting results for the 2D Bazhanov-Stroganov model have been obtained (joint work with S.Pakuliak and S.Sergeev).

Nenad Manojlovic  Transparencies (pdf)

Twisted Gaudin Models

The Gaudin models are reviewed by analyzing model related to the twisted
rational sl(2) classical $r$-matrix. The eigenvectors of the corresponding Gaudin Hamiltonians are found using explicitly constructed annihilation operators. The commutation relations between the annihilation creation operators the generators of the relevant loop algebra are calculated. The coordinate representation of the Bethe states is presented, as well as the relation between the Bethe vectors and solutions to the Knizhnik-Zamolodchikov equation.

Jasbir Nagi  Transparencies (pdf)

Logarithmic Superconformal Field Theory

The construction of Logarithmic Primary Fields is a
subject well understood, now, for sometime. In this talk, I review
constructions, and extend them to the N=1,2 supersymmetric case.

Thomas Quella  Transparencies (pdf)

Permutation branes in WZW models GxG

We employ the Dirac-Born-Infeld and the Lagrangian description to
motivate the existence of new branes which are generalizations of the usual permutation branes on GxG which solely exist for equal levels. The
geometries and cohomological properties of these branes give a natural
explanation for the K-theoretic charges in product groups (and in
particular for SU(2)xSU(2)) of different size for which no carriers could be identified before. From an abstract point of view these branes should give rise to new defect lines between conformal field theories with different central charge.

Fedor Smirnov Transparencies (pdf)

Correlation functions in lattice integrable models

Charles Young  Transparencies (pdf)

Non-local charges, graded Lie algebras and coset space actions