Gernot Akemann

Low Energy Constants in QCD from Matrix Models

Chiral Perturbation Theory (XPT), the low energy effective theory of QCD, becomes equivalent to an integrable chiral Random Matrix Theory (chRMT) in a particular finite volume limit. The low energy constants in XPT can then be extracted by comparing QCD Lattice results to the analytic predictions from chRMT (or XPT). Universal chRMT results are reviewed relevant for QCD Dirac operator spectra with and without quark chemical potential.

Niklas Beisert

Integrability in AdS/CFT, the Hubbard Model and Quantum Algebra

The worldsheet scattering matrix of AdS/CFT or equivalently the R-matrix for the one-dimensional Hubbard model appear to be exceptional solutions of the Yang-Baxter equations. We review recent progress in unraveling the algebraic structures underlying this R/S-matrix in terms of a classical bialgebra, Yangians and quantum-deformed algebras.

Hermann Boos

Factorization of correlation functions and fermionic structure of the XXZ model

We discuss a phenomenon of factorization of the correlation functions for the XXZ spin chain with disorder field. We introduce a space of quasi-local operators and an exponential formula for the corresponding correlation functions. The wholealgebraic information is gathered in the b- and c-operatorswhich have the meaning of fermionic annihilation operators. In analogy with CFT the disorder field itself is consideredas a "primary field" which plays the role of a vacuum wrtthe above annihilation operators. We also introduce fermionic creation operators which together with annihilation operators satisfy the canonical anti-commutation relations. With the help of the creation operators we construct a special basis in the space of quasi-local operators for which the correlation functions have a simple determinant form.

Nils Carqueville

Triangle-generation in topological D-brane categories

Tachyon condensation in topological Landau-Ginzburg models which correspond to topological N=2 CFTs can generally be studied using methods of commutative algebra and properties of triangulated categories. Within the formulation through matrix factorisations, this allows for detailed studies of generation processes of D-brane systems in all minimal models of type ADE, as well as many more complicated models.

Paul Fendley

Topological order for quantum loops and nets

I discuss models of quantum loops and nets that have ground states with topological order. This means the ground state is a sum over geometric objects of all length scales. These models have a quantum self-duality, making it possible to find a simple Hamiltonian preserving the topological order. Even though these are two-dimensional quantum systems (and so in 2+1 dimensional spacetime), establishing these results requires exploiting integrability and conformal field theory for two-dimensional classical systems.

Paulo Goncalves de Assis

Non-Hermitian Hamiltonians of Lie algebraic type

I will give a brief general introduction to pseudo-Hermitian Hamiltonian systems. Taking solvable models of Lie algebraic type as a motivating starting point we study systematically a class of non-Hermitian Hamiltonians with real spectra, which are bilinear in the generators of an su(1,1) algebra. We construct a metric operator and isospectral Hermitian counterparts for these Hamiltonians. Alternatively we employ a generalized Bogoliubov transformation for these type of Hamiltonians, which does not only allow to compute the eigenspectra, but in addition provides the explicit PT-symmetric eigenstates. I provide some examples of concrete representations for these algebras.

Ingo Runkel

Fusion hierarchies and defects lines

Fusion hierarchies first appeared in the study integrable lattice models such as restricted height models. Starting from the transfer matrix of the model one constructs a family of operators which mutually commute and obey a functional relation. It turns out that one can find similar functional relations directly in the continuum conformal field theory. One approach to do this is based on a free field construction due to Bazhanov, Lukyanov and Zamolodchikov. A related approach is to consider defect lines perturbed by defect fields.

Charles Young

Identical particles in kappa-deformed quantum field theory

There exists a family of deformations of Minkowski spacetime, and its Poincare symmetries, parameterized by a mass-scale kappa. Understanding kappa-deformed quantum field theory poses an interesting challenge. I will discuss some recent work on one aspect of the problem: defining particle-exchange, and hence identical particles, in a kappa-covariant fashion.