# Invited talks

## Balog, Janos

*LWW coupling in integrable models*

Exact calculation of the LWW coupling (finite volume particle mass) in the integrable O(n) nonlinear sigma model is presented using the proposed excited state TBA equations. The results are compared to lattice Monte Carlo measurements of the same quantity and help clarifying issues related to the functional form of cutoff effects on the lattice. An alternative to the (infinite) set of TBA equations, the NLIE method is also discussed.

## Bauer, Michel

*From conformal field theory to stochastic Loewner evolutions and back*

## Cappelli, Andrea

*Matrix model description of quantum Hall states*

## Corrigan, Ed

*Aspects of defects*

## Dorey, Patrick

*g-functions as probes of boundary conformal field theories*

## Gawedzki, Krzysztof

*WZW branes and gerbes*

## Kostov, Ivan

*Instantons in non-critical string theories and matrix models*

The non-perturbative corrections to the free energy of the two-matrix model are expressed in terms of its spectral curve. The eigenvalue instantons are associated with the vanishing cycles of the curve. Compared with the world-sheet theory, the results for the (p,q) critical points lead to intriguing identifications between different Liouville and matter boundary conditions in non-critical string theories.

## Miramontes, J. Luis

*Mass scales and crossover phenomena in the homogeneous sine-Gordon models*

The finite-size behaviours of the homogeneous sine-Gordon models are analysed in detail, using the thermodynamic Bethe ansatz. Crossovers are observed which allow scales associated with both stable and unstable quantum particles to be picked up. We show that these match precisely with the mass scales found classically, supporting the idea that the full set of unstable particle states persists even far from the semiclassical regime. We comment on the Lagrangian treatment of the theories, novel issues which arise in the form-factor approach for theories with unstable particles, and the role of heterotic cosets in the staircase flows exhibited by the HSG models.

## Mussardo, Giuseppe

*Breaking integrability*

## Nissimov, Emil

*Weyl-invariant light-like branes*

We propose a new class of p-brane theories which are Weyl-conformally invariant for any p. For any odd world-volume dimension the latter describe intrinsically light-like branes, hence the name WILL-branes (Weyl-Invariant Light-Like branes). Next we discuss the dynamics of WILL-membranes (i.e., for p=2) in various external physically relevant D=4 gravitational backgrounds. In the case of Schwarzschild and Reissner-Nordstroem black holes we find that the WILL-membrane materializes the event horizon.

## Ravanini, Francesco

*Excited states NLIE for sine-Gordon model in a strip with Dirichlet boundary conditions*

We investigate various excited states of Sine-Gordon model on a strip with Dirichlet boundary conditions on both boundaries using a Non-Linear Integral Equation (NLIE) approach.

## Riva, Valentina

*Semiclassical study of finite-size effects in two-dimensional quantum field theories*

We present recent results obtained in collaboration with G. Mussardo and G. Sotkov, regarding finite-size effects in two-dimensional massive quantum field theories, both integrable and non-integrable. A non-perturbative analytical study of this problem can be performed by implementing on a finite geometry the semiclassical quantization of kink backgrounds. Choosing as illustrative examples the sine-Gordon and the broken phi^4 theories, we show how the kinks are realized on the cylinder, directly providing an estimate of the spectral representation of correlation functions. We then explicitly perform the complete semiclassical quantization in the one-kink sector of the sine-Gordon model, and discuss the corresponding scaling functions. Finally, we extend the above ideas to the case with boundaries, describing the sine-Gordon model on a strip with Dirichlet boundary conditions at both edges.

## Schomerus, Volker

*Non-Hermitian Liouville theory*

## Sokatchev, Emery

*Three-loop test of the dilatation operator in N=4 super-Yang-Mills*

## Taormina, Anne

*Beyond rational conformal field Theory*

## Zamolodchikov, Alexey

*Fixed area partition function in Liouville gravity*

# Short talks

## Arnaudon, Daniel

*On integrable open spin chain*

## Caselle, Michele

*Quantitative biology and integrable models*

## Castro Alvaredo, Olalla

*Chaos in the thermodynamic Bethe ansatz*

We investigate the discretized version of the thermodynamic Bethe ansatz equation for a variety of 1+1 dimensional quantum field theories. By computing Lyapunov exponents we establish that many systems of this type exhibit chaotic behaviour, in the sense that their orbits through fixed points are extremely sensitive with regard to the initial conditions.

## Caudrelier, Vincent

*Quantum non-linear Schroedinger equation with impurity.*

We present the construction of the exact second quantized solution of the nonlinear Schrodinger equation in the presence of a reflecting and transmitting impurity. This relies on the concept of Reflection-Transmission algebra. We also discuss some physical issue such as correlation functions and the scattering matrix.

## Controzzi, Davide

*New results on the O(3) non-linear sigma model with topological term*

## Crooks, David

*D-brane probes in Klebanov-Witten*

We compute the killing spinors of the Klebenov-Witten model, and derive conditions for kappa symmetric D7-Brane and D3-Brane probes.

## Feverati, Giovanni

*Integrals of motion from TBA and lattice-conformal dictionary*

The integrals of motion of the tricritical Ising model are obtained by Thermodynamic Bethe Ansatz (TBA) equations derived from the $A_4$ integrable lattice model. They are compared with those given by the conformal field theory leading to a unique one-to-one lattice-conformal correspondence. They can also be followed along the renormalization group flows generated by the action of the boundary field $\varphi_{1,3}$ on conformal boundary conditions in close analogy to the usual TBA description of energies.

## Hoshino, Yuichi

*Infrared catastrophe in QED3*

Infrared behaviour of charged particle propagator in QED3 is determined based on spectral representation with LSZ reduction formula . Lowest order spectral function contains gauge invariant position depedent mass and Coulomb energy. The former leads to strong dumping of the propagator at large distance and the latter acts as wave function renormalization such as renormalization group. There exist condensation of pair in which the the propagator is localized in the finite region with finite infrared cut-off.We obtain the dispersion integrals for the momentum space propagator numerically. In the limit of zero infrared cut-off propagator in momentum space vanishes ,which is proportional to cut-off with logarithmic correction.

## Ishimoto, Yukitaka

*Logarithmic correlation functions in minimal string theory*

## Karowski, Michael

*Form factors for Toda and Z(N) Models*

## Kojima, Takeo

*The correlation function of the $k$-fusion 8 vertex model*

We study the $k$-fusion 8 vertex model, which is a higher spin generalization of Baxter's 8 vertex model. Our considering $k$-fusion hierarchy contains Fateev's $21$-vertex model as $k=2$-fusion model. We are interested in the integral representations of the correlation functions. Our analysis is based on the vertex-face correspondence, which enables us to express the correlation function of the vertex model in terms of face model. Following Baxter's corner transfer matrix method, we express the correlation function by the trace of the vertex operator of the $k$-fusion SOS model and 'tail-operator'. We give free field realizations of this vertex operator and 'tail operator', and construct integral representations of the correlation functions. This talk gives a generalization of Lashkevich and Pugai's theory on Baxter's 8 vertex model : {it Nucl.Phys.}{f B516}, 623-651 (1998). This talk is based on the collaboration with Hitoshi Konno and Robert Weston.

## Kryukov, Sergei

*Special integrals of motion in quantum integrable systems and Dirac quantization of the massless Thirring model: energy-momentum tensor anomaly*

We investigate quantum integrals of motion in the sine-Gordon, Zhiber-Shabat and similar systems. When the coupling constants in these models take special values a new quantum symmetry appears. In those cases, correlation functions can be obtained, and they have a power law behavior. The Dirac method of quantizing Hamiltonian systems with constraints is applied to the massless Thirring model. We solve the quantum Hamiltonian equation for the energy-momentum tensor and obtain a violation of the classical conservation law. A previously noticed problem with the equal-time anticommutators can be fixed using this Hamiltonian method.

## Nagi, Jasbir

*Superconfomal primary fields on a graded Riemann sphere*

The construction of a primary field as a geometric object on a Riemann Sphere has been understood for a while now. One can associate anticommuting co-ordinates on a Riemann Sphere using a Graded Riemann Sphere construction. It is then possible to define a primary superfield as a geometric object on this space.

## Nagy, Zoltan

*Dynamical quadratic algebras*

We propose a dynamical extension of the quantum quadratic exchange algebras introduced by Freidel and Maillet and discuss its fusion and comudule structures in view of obtaining a set of commuting hamiltonians.

## Niccoli, Giuliano

*Matrix elements of the operator T\bar{T} in integrable quantum field theory*

Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if the theory is integrable the addition of a requirement of factorization at high energies can lead to the exact determination of the generic matrix element of this operator on the asymptotic states. The construction is performed explicitly in the Lee-Yang model.

## Nichols, Alexander

*Surprises in spin chain spectra and the boundary Temperley-Lieb algebra*

I shall discuss a rather surprising equivalence between the spectra of the XXZ model with an arbitrary left boundary term and the same XXZ model with two diagonal boundary terms. I shall explain some of the subtleties in this equivalence and illustrate the underlying role of the boundary Temperley-Lieb algebra and its representation theory.

## Nikolov, Nikolay

*Vertex algebras in higher dimensions and globally conformal invariant quantum field theory*

We propose an extension of the definition of vertex algebras in arbitrary space-time dimensions together with their basic structure theory. A one-to-one correspondence between these vertex algebras and axiomatic quantum field theory (QFT) with global conformal invariance (GCI) is constructed. (hep-th/0307235, to appear in Commun. Math. Phys.)

## Parashar, Deepak

*On coloured quantum groups, quantum plane and Yang-Baxter operators*

The notion of quantum groups has, in recent years, been generalised by parametrizing the corresponding generators with some continuously varying 'colour' variables and the associated algebra and the coalgebra are defined in a way that all Hopf algebraic properties remain preserved. This results in the coloured extension of a quantum group. Focussing on the most intuitive example of $GL_q(2)$, I will present basic results from the theory of coloured quantum groups such as establishing the picture of duality, constructing differential calculi, and exhibiting the quantum plane covariant under the action of coloured $GL_q(2)$. Further, the algebraic notion of Yang-Baxter operators is generalised to yield classes of "coloured" Yang-Baxter operators.

## Ragoucy, Eric

*RT-algebras and the non-linear Schroedinger equation with impurity*

We present the second quantized solution to the Non-linear Schrodinger equation on a line with an impurity at origin.The resolution uses a RT-algebra formalism which we introduce first.

## Ribault, Sylvain

*Non-rational CFT*

## Sanchez-Guillen, Joaquin

*Analytical and numerical results for quntum field theories on the world line*

World line methods are presented with new results for Scalar QED and Yukawa theories in four dimensions. Exact results for fermions are also given in lower dimensions.

## Sorba, Paul

*Finite temperature quantum field theory with impurities*

We apply the concept of reflection-transmission (RT) algebra, originally developed in the context of integrable systems in 1+1 space-time dim.,to the study of finite temperature quantum field theory with impurities in higher dimensions. The interaction of a scalar field in (s+1)+1 space-time dim., with impurities localized on s-dim.hyperplanes is discussed. We consider first the case s=0 and extend afterwards all results to s not 0. Constructing the Gibbs state over an appropriate RT algebra, we derive the energy density at finite temperature and establish the correction to the Stefan-Boltzmann law generated by the impurity. The contribution of the impurity bound states is taken into account. The charge density profiles for various impurities are also investigated. This is a joined work with M.Mintchev: hep-th/0405264, published in JSTAT (2004)PO7001.

## Toth, Gabor Zsolt

*On N=1 supersymmetric boundary bootstrap*

## Zarembo, Konstantin

*Integrability and AdS/CFT*

Integrability arises as a hidden symmetry on both sides of the AdS/CFT duality, a conjectured equivalence of conformal N=4 supersymmetric Yang-Mills theory in four dimensions to string theory in Ante-de-Sitter space. The integrability proved to be a powerful tool in exploring consequences of the AdS/CFT duality and potentially can lead the way to the exact solution of the AdS/CFT correspondence.