RAQIS'12: Talks, posters and PDFs

**AUFGEBAUER Britta **
* Finite temperature correlation functions from discrete functional equations
*

We present an approach to the static finite temperature correlation functions of the Heisenberg chain based on functional equations. An inhomogeneous generalization of the n-site density operator is considered. The lattice path integral formulation with a finite but arbitrary Trotter number allows to derive a set of discrete functional equations with respect to the spectral parameters. We show that these equations yield a unique characterisation of the density operator. Our functional equations are a discrete version of the reduced q-Knizhnik-Zamolodchikov equations which played a central role in the study of the zero temperature case.

Pdf file of the presentation

**AVAN Jean **
* Dynamical reflection algebras: examples from Calogero-Moser models
*

The presence of boundaries to a quantum integrable system imposes to
complement the Yang-Baxter algebra RTT = TTR by the boundary equation RKRK = KRKR. In parallel
consistent deformations of the YB algebra have been defined, leading
to so-called dynamical Yang Baxter equations. The association of both
structures yields so-called dynamical boundary algebras. Two such structures were known until last year when we constructed a third one. We will describe this new algebraic structure and unravel its connection with
the higher Poisson structures of the Calogero-Moser model, focusing on the
rational potential case v(r) = 1/r^{2}.

Pdf file of the presentation

**BALOG Janos **
* Hybrid-NLIE for the AdS/CFT spectral problem
*

Hybrid-NLIE equations, an alternative finite NLIE description for the spectral problem of the super sigma model of AdS/CFT and its gamma-deformations are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT TBA equations by a few appropriately chosen complex NLIE variables, which are coupled among themselves and to the Y-functions associated to the remaining central nodes of the TBA diagram. Our equations differ substantially from the recently published finite FiNLIE formulation of the spectral problem.

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**BELAVIN Alexander **
* Instantons and bases in CFT
*

We use AGT correspondence for the construction of the bases of OPE in Conformal field theory

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**BELLIARD Samuel **
* SU(3) Bethe vectors
*

Different formulations of SU(3) Bethe vectors will be presented.
The action of the generators of the Yangian on these vectors will be given.
These results are important for the calculation of form factors and correlation functions
from the quantum inverse scattering problem and scalar products of Bethe vectors.
This is a joint work with S. Pakuliak, E. Ragoucy and N. Slavnov.

Pdf file of the presentation

**BYTSKO Andrei **
* Tetrahedral Y-systems
*

Using a solution to the Zamolodchikov tetrahedron equation, we construct an identity involving quantum dilogarithms. Suitable reductions of this identity yield quantum dilogarithm identities related to Y-systems of the A-type.

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**CAUDRELIER Vincent **
* Electronic transport on quantum graphs
*

Combining the formalism of integrable quantum field theory with results from the theory of quantum graphs, we will present a general framework to describe electronic transport on arbitrary geometries that can be modeled by quantum graphs. In particular, the formalism allows for the computation of equilibrium and out of equilibrium correlation functions at finite temperature and with an external magnetic field. This is interesting in view of applications to networks of quantum wires. As an illustration, we will present results for the conductance and the noise in a quantum ring pierced by a magnetic flux and connected to three (or more) thermal reservoirs.

**CHENG Zhang **
* Yang-Baxter and reflection maps from factorization of vector soliton interactions on the half-line
*

We consider the Vector Nonlinear Schrödinger equation on the half-line. First via a Bäcklund transformation method, we derive two classes of integrable boundary conditions, a mirror image technique is applied to compute exact soliton solution. Then using dressing transformations, factorization of soliton-soliton and soliton-boundary interactions is showed. Soliton interactions correspond to so-called Yang-Baxter map which are solutions of the set-theoretical Yang-Baxter equation. We introduce a new mathematical object, which we call reflection map corresponding to soliton-boundary interaction, that satisfies the set-theoretical reflection equation, which we also introduce. Basic aspects of reflection map are discussed.

**DE LEEUW Marius **
* Quantum deformations in AdS/CFT *

In this talk I will discuss the quantum deformed su(2|2) algebra. This
superalgebra describes a quantum deformed version of the Hubbard model and the
corresponding S-matrix is closely related to the S-matrix of the AdS5xS5
superstring. I will introduce the algebra, highlight some of its features and
discuss some applications in the context of the AdS/CFT correspondence.

Pdf file of the presentation

**DOBREV Vladimir **
* Group-Theoretical Classification of BPS States in D=4 Conformal Supersymmetry
*

We give explicitly the reduction of supersymmetries of the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using this we give the classification of BPS and possibly protected states.

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**DOYON Benjamin **
* Quantum steady states out of equilibrium
*

Quantum steady states out of equilibrium are states admitting a nonzero constant local current density. In many-body integrable systems, there are infinitely-many local conserved charges, hence current densities. I will explain how to describe the associated steady states in integrable systems. These steady states emerge after connecting two baths with different chemical potentials associated to the conserved charges. The description is valid both in spin chains and in quantum field theory (i.e. near their critical points). Specialising to the energy flow, I will describe the consequences in conformal field theory (non-equilibrium CFT), and in the Ising quantum field theory (non-equilibrium form factors). Various parts of this work are done in collaboration with Denis Bernard and my students Yixiong Chen and Marianne Hoogeveen.

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**DUGAVE Maxime **
* Form factors for the XXZ chain and non-linear integral equations
*

We have worked out exact expressions for the thermal
form factors of the XXZ chain. This poster is based on
joint work with Frank Goehmann and is related to his talk.

Pdf file of the presentation

**FADDEEV Ludwig D **
* A survey on modular quantum dilogarithm
*

TBA

**FEIGIN Misha **
* Generalized Macdonald-Mehta integrals and Baker-Akhiezer functions
*

We consider Baker-Akhiezer functions associated with the special arrangements of hyperplanes with multiplicities; these are particular eigenfunctions for the generalized Calogero-Moser operators. We establish integral identity for the Baker-Akhiezer functions that may be viewed as a generalization of the self-duality property of the usual Gaussian with respect to the Fourier transformation. We derive that the value of the Baker-Akhiezer function at the origin is given by the integral of Macdonald-Mehta type. In contrast to the standard Macdonald-Mehta integrals arising in random matrix theory our integrand has singularities on the arrangement so a regularisation is needed. We explicitly compute these regularised integrals for known Coxeter and non-Coxeter arrangements admitting the Baker-Akhiezer functions. In the Coxeter cases we use analytic continuation of the usual Macdonald-Mehta integral. In the two-dimensional examples we use the explicit form of the Baker-Akhiezer functions found by Berest, Cramer and Eshmatov. In the higher-dimensional non-Coxeter examples we evaluate these integrals by taking a special limit of the Dotsenko-Fateev integral arising in conformal field theory. This is a joint work with M.A. Hallnas and A.P.Veselov.

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**FINCH Peter **
* Excitations of the integrable D(D3) anyon chain
*

In this talk I will consider integrable quantum chains constructed from the quasi-triangular Hopf algebra DD3. The conformal field theories along with the excitation spectra are presented for the periodic chain in the usual spin basis as well as in a fusion path (anyon) basis.

**FODA Omar **
* Slavnov scalar products in Yang-Mills theories
*

I would like to review how Slavnov scalar products are used to compute tree-level and 1-loop 3-point functions in su(2) integrable sectors in planar Yang-Mills theories with various supersymmetries including QCD.

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**FOERSTER Angela **
* Exactly solvable models and ultracold atoms
*

We investigate some Bethe ansatz integrable models in the context of ultracold atom systems. First we briefly discuss the integrability and mathematical construction of some simple models. Then exactly solvable models of ultracold Fermi gases are examined through the thermodynamic Bethe Ansatz. and the phase diagrams of two- and three-component one-dimensional attractive fermions with population imbalance are obtained. The results for the strong coupling regime provide a description of the quantum phases which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes [1,2]. In addition, other integrable models relevant in this ultracold scenario, such as spin-1 bosons in a 1D harmonic trap are also investigated and the phase diagrams and density profiles are obtained [3].

[1] Phase Diagrams of Three-Component Attractive Ultracold Fermions in One-Dimension, C.C. N. Kuhn and A. Foerster New J. Phys. 14 (2012) 013008 [2] Exactly solvable models and ultracold Fermi gases, C.C. N. Kuhn, X. W. Guan, A. Foerster and M. Batchelor J. Stat. Mech. (2010) P12014 [3] Quantum criticality of spin-1 bosons in a 1D harmonic trap, C.C. N. Kuhn, X. W. Guan, A. Foerster and M. Batchelor arXiv:1111.2375.

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**FONSECA Tiago **
* Higher Spin Generalization of the 6-Vertex Model and Macdonald Polynomials
*

It is known that the 6-Vertex model is a quantum integrable model, therefore we know, at least in theory, everything about it. For example, in the case of Domain Wall Boundary Conditions, the partition function is a relatively simple determinant (Izergin, 1987) and it is related to a Schur polynomial. In a more recent work, Caradoc, Foda and Kitanine (2006) tell us how to generalize this result for higher spins. Based in their work, one can prove that the new partition function is related to a Macdonald polynomial (dF and Balogh, to appear). In this talk, I will describe the 6-vertex model, explain how to create the higher spin model from the original model. And finally, I will sketch how one can prove that this is indeed a Macdonald polynomial.

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**GAINUTDINOV Azat **
* A limit of affine Temperley-Lieb algebras at a root of unity and bulk logarithmic CFT
*

We study spin-chains based on affine Temperley-Lieb (TL) algebras and their centralizer constructions at a root of unity case. An analogue of the Howe dulaity in such systems allowed to take the direct limit of these spin-chains when the number of tensorands (sites) goes to infinity. The limit of the representation spaces turns out to be a logarithmic conformal field theory in the bulk, while the affine TL algebra in the limit is expressed by a representation of the affine Lie algebra of infinite rank sp_{∞} and contains left and right Virasoro algebras. The description of this limit in field-theoretic terms led us to a notion of the interchiral algebra generalizing chiral algebras in the non-chiral (bulk) case.

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**GEPNER Doron **
*Nonstandard parafermions and string compactification *

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**GOMES Jose Francisco **
* The higher grading structure of the WKI hierarchy and the two-component short pulse equation.
*

A higher grading affine algebraic construction of integrable hierarchies, containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is proposed. We show that a two-component generalization of the Schäfer-Wayne short pulse equation arises quite naturally from the first negative flow of the WKI hierarchy. The conserved charges, both local and nonlocal, are obtained from the Riccati form of the spectral problem. The loop-soliton solutions of the WKI hierarchy are systematically constructed through gauge followed by reciprocal Bäcklund transformation, establishing the precise connection between the whole WKI and AKNS hierarchies. The connection between the short pulse equation with the sine-Gordon model is extended to a correspondence between the two-component short pulse equation and the Lund-Regge model.

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**GOEHMANN Frank **
* Form factors of the quantum transfer matrix and asymptotics of temperature correlators of the XXZ chain *

We have derived expressions for the form factors of the
quantum transfer matrix of the spin-1/2 XXZ chain
which allow us to take the limit of an infinite Trotter
number. These form factors determine the finitely many
amplitudes in the leading asymptotics of the finite
temperature correlation functions of the model.
We consider the longitudinal as well as the transversal
two-point correlation functions and also indicate how our
formulae have to be modified to cover the case of
ground state correlation functions of finite length
chains. In the temperature case we show how known
results for the high-temperature asymptotics are
recovered from the form factor expansion. In the
zero-temperature limit we show by example how to obtain
the `critical behaviour' of the form factors from our
formulae. This talk is based on joint work with Maxime
Dugave.

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**JIMBO Michio **
* Representations of quantum toroidal algebras: Recent topics *

Quantum toroidal algebras were first introduced in 1995 as further affinization of the quantum affine algebras. In the type A case, basic structure theory has been established by Miki. However their representation theory remains largely open. Here we explain an elementary construction of a new family of representations, in which bases are parametrized by combinatorial objects (ordinary or plane partitions) and the matrix coefficients for the generators are given in factorized form. This talk is based on joint works with Feigin, Miwa and Mukhin.

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**KAZAKOV Vladimir **
* Classical integrability for quantum spin chains and sigma models
*

I will review recent advances in applications of classical Hirota dynamics for the analysis and solution of quantum integrable systems. In quantum (super)spin chains, it allows to interpret the (eigenvalues of) transfer matrices as special type of mKP tau-functions and give a new construction of Baxter's Q-functions. In sigma-models, such as principal chiral field or the superstring model related to AdS/CFT duality, it allows to efficiently reduce the spectral Y-system related to TBA, to a finite non-linear system of integral equations (FiNLIE).

**KLUEMPER Andreas **
* Correlation functions for integrable higher spin su(2) quantum chains
*

We use the unique characterisation of density operators of inte-
grable su(2) quantum chains by suitable functional equations. The
lattice path integral formulation with a finite but arbitrary Trotter
number allows to derive a set of discrete functional equations and an-
alytical properties with respect to the spectral parameters. The n-site
density operator is considered for integrable higher spin-S quantum
chains at arbitrary temperature T . Explicit results are given for the
case of S = 1 and n = 2 and 3 in terms of non-linear and associated lin-
ear integral equations avoiding the multiple integral expressions previ-
ously derived in the literature. The correlation functions on arbitrarily
many n sites factorize similarly to the by now well understood spin-1/2
case.

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**KONNO Hitoshi **
* Elliptic Quantum Groups U _{q,p} and E_{τ,η;}
*

Up to now, we know three formulations of the face type elliptic quantum group, B

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**KORFF Christian **
* The quantum Ablowitz-Ladik model: completeness of the Bethe ansatz
*

We discuss a discrete version of the quantum nonlinear Schr"odinger model, the quantum Ablowitz-Ladik model, and give a completeness proof of the algebraic Bethe ansatz. Using this result we establish an algebra isomorphism between the conserved charges of the model and an affine version of the spherical Hecke algebra. In the crystal (strong coupling) limit this algebra becomes the Verlinde or fusion algebra of the su(n) WZW model.

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**KOZLOWSKI Karol **
* Surface Free energy of the open XXZ spin-1/2 chain.
*

In this talk, I will report on the possibility to represent the finite Trotter number approximant of the surface free energy of the open XXZ spin-1/2 chain subject to diagonal boundary fields in terms of Tsuchiya determinants. I will explain how to take the infinite Trotter limit of such expressions. This provides an expression for the surface free energy of the open chain in terms of series of multiple integrals. This integral representation allows one to extract the low-temperature asymptotic behavior of the boundary magnetization at finite external magnetic field. This is a joint work with B. Pozsgay.

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**KULISH Petr **
* Integrable spin systems and representation theory *

Quantum integrable spin chains are related to classical and quantum
Lie (super-) algebras and their finite and infinite dimentional
representations. It is pointed out that with appropriate boundary
condition (open spin chains) corresponding algebra can be identified
with the symmetry algebra of integrals of motion (transfer matrix).
According to a generalized Schur - Weyl duality this yields a multiplet
structure of the spectrum and invariant subspaces. This approach
includes spin chains related to non-quasiclassical quantum algebras
as well.

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**LISOVYY Oleg **
* Conformal field theory of Painlevé VI*

Generic Painlevé VI tau function τ(t) may be interpreted as
four-point correlator of primary fields of arbitrary dimensions in 2D CFT
with c=1. Full and completely explicit expansion of τ(t) near the
singular points can thus be obtained using AGT combinatorial
representation of conformal blocks and determining the corresponding
structure constants..

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**MALLICK Kirone **
* Current fluctuations in the exclusion process *

The asymmetric simple exclusion process is a model used as a
template to study various aspects of non-equilibrium statistical physics.
It appears as a building block in more realistic descriptions
for low-dimensional transport with constraints. In the steady state, a
non-vanishing current is carried through the system. The statistical
properties of this current are archetypal observables for non-equilibrium
behaviour. It this talk, we explain how to derive the full statistics
of the current in the ASEP. We present exact combinatorial formulas
valid for all system sizes and all values of the system parameters.
Our results are obtained using integrability techniques borrowed
from the theory of quantum integrable systems such as the Bethe Ansatz
and the Matrix Product Representation.

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**MATSUI Chihiro **
* The ground state of SUSY sine-Gordon model with the Dirichlet boundary conditions via lattice regularization
*

We discuss the ground state of SUSY sine-Gordon model with the Dirichlet boundary conditions via the lattice regularization. The Bethe roots which characterize the ground state are specified from the nonlinear integral equations, which are found to have different forms depending on the value of boundary parameters. The boundary energy is calculated based on the analyticity of the transfer matrices.

**MIRAMONTES J Luis **
* Aspects of the q-deformed AdS(5)x S(5) superstring S-matrix
*

I will review recent work aimed to the construction of an S-matrix theory that interpolates between the usual non-relativistic AdS(5)xS(5) superstring S-matrix and the relativistic S-matrix corresponding to its Pohlmeyer reduction. The talk will be based on arXiv:1206.0010, arXiv:1112.4485 and arXiv:1107.0628.

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**MOTEGI Kohei **
* Exact relaxation dynamics in the totally asymmetric simple exclusion process
*

We study the exact relaxation dynamics of the totally asymmetric simple exclusion process on a ring. The full relaxation dynamics of the local densities and currents are examined by the algebraic Bethe ansatz method. Moreover, we find the scaling exponents of the asymptotic amplitudes. We also find that the relaxation times starting from the step and alternating initial conditions are governed by different eigenvalues of the Markov matrix. This is based on joint work with K. Sakai and J. Sato.

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**NIEMI Antti **
* Discrete Nonlinear Schrödinger Equation and Polygonal Solitons with Applications to Collapsed Proteins
*

We introduce a novel generalization of the integrable discrete nonlinear Schrodinger equation. It supports dark solitons that we utilize to model proteins in the biologically active collapsed phase. As an example we consider the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. We use its backbone as a template to explicitely construct a two soliton configuration. Each of the two solitons describe well over 7.000 supersecondary structures of folded proteins in the Protein Data Bank with sub-Angstrom precision. Our results suggest that these new solitons are abundant in nature.

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**OSHIMA Kazuyuki **
* The Elliptic Algebra U _{q,p}(B_{N}^{(1)}) and Vertex Operators
*

We introduce an elliptic quantum algebra of type B

**PALMAI Tamas **
* Sine-Gordon form factors in finite volume
*

We verify exact form factors coming from bootstrap in the sine-Gordon model, a prototype theory with nondiagonal scattering. This is achieved by finding convincing agreement between finite volume form factors calculated from the truncated conformal space approach and from bootstrap via results of the finite volume form factor program. Evaluation of the nontrivial multi-soliton form factors is made possible by a newly developed regularization scheme.

**ROLLET Geneviève **
* Classification of Non-Affine Non-Hecke Dynamical R-Matrices
*

A complete classification of non-affine dynamical quantum R-matrices obeying the Gl_{n}(C)-Gervais-Neveu-Felder equation is given without assuming either Hecke or weak Hecke conditions. More general dynamical dependences are observed. It is shown that any solution is built upon elementary blocks, which individually satisfy the weak Hecke condition. Each solution is in particular characterized by an arbitrary partition of the set of indices {1..n} into classes and an arbitrary family of signs on this partition. The weak Hecke-type R-matrices exhibit an analytical behaviour with general trigonometric or rational dynamical dependencies (arXiv:1204.2746v2).

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**SAKAI Kazumitsu **
* Multiple Schramm-Loewner evolutions for conformal field theories with Lie algebra symmetries
*

We provide multiple Schramm-Loewner evolutions (SLE) to describe the scaling limit of multiple interfaces in critical lattice models possessing Lie algebra symmetries. The critical behavior of the models are described by Wess-Zumino-Witten (WZW) models. Introducing a multiple Brownian motion on a Lie group as well as that on the real line, we construct a multiple SLE with the additional Lie algebra symmetry. The connection between the resultant SLE and the WZW model can be understood via SLE martingales satisfied by the correlation functions in the WZW model. Due to interactions among SLE interfaces, these Brownian motions have drift terms which are determined by partition functions for the corresponding WZW model. By analyzing the correlation functions, we also discuss the topology of configurations of the SLE curves.

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**SKRYPNYK Taras **
* Quantum integrable systems and classical non-skew -symmetric r-matrices
*

We will make a review of a recent advances in the theory of quantum integrable systems associated with non-skew-symmetric classical r-matrices. Such the systems, in general, are not connected with the quantum qroups or related structure and constitute a separate family of integrable models. We will illustrate our approach on the examples of integrable spin systems of the generalized Gaudin type, integrable boson and spin-boson systems. We will present the physical applications of the obtained integrable models, in particular, to BCS-type models (theory of superconductivity), Jaynes-Cummings-Dicke-type models and Bose-Hubbard-type dimers (quantum optics). We will consider in details the case of classical elliptic r-matrices and the corresponding quantum integrable models.

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**SLAVNOV Nikita **
* Algebraic Bethe ansatz for scalar products in SU(3)-invariant models
*

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of XXX SU(3)-invariant Heisenberg chain.

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**TERRAS Véronique **
* ABA approach to correlation functions of the cyclic SOS model *

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**VICEDO Benoit **
* Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
*

The property of non-ultralocality in certain classically integrable field theories is known to pose a serious obstacle to quantization. A way around this problem was proposed in '86 by Faddeev and Reshetikhin in the case of the principal chiral model on SU(2). Their procedure begins by replacing the problematic non-ultralocal Poisson brackets by ultralocal ones and modifying the corresponding Hamiltonian to reproduce the same dynamics. I will show how these first steps maybe be generalized to symmetric space sigma-models. The modified theory in this case is classically equivalent to the Pohlmeyer reduction of the original sigma-model and is described by a gauged Wess-Zumino-Witten action with an integrable potential. I will discuss the first steps towards constructing an integrable lattice discretization of these latter models. (based on arXiv:1204.0766, 1204.2531, 1206.6050)

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**VOLKOV Alexander **
* Tetrahedral Y-system *

TBA

**WHEELER Michael **
* Factorization formula for SU(3) scalar products
*

The calculation of scalar products between Bethe vectors is an important topic of quantum integrable models. In the case when both vectors are on-shell, the scalar product is the norm-squared of the Bethe eigenstate. More generally, off-shell scalar products (in which one vector is not an eigenvector of the transfer matrix) are important to the study of correlation functions. In the case of models based on the SU(2)-invariant R-matrix, it is known from the work of N. Slavnov that certain off-shell scalar products have a determinant expression. A difficult unsolved problem is the generalization of Slavnov's formula to models based on SU(n). This talk will describe recent work on the SU(3) problem, where it was shown that by sending half of the Bethe variables in the scalar product to infinity, it factorizes into a product of two determinants.

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**YAMADA Yuji **
* Classification of solutions to the reflection equation
*

We classify and list up all the meromorphic solutions K(z) to the reflection equation associated to the critical ** Z**_{N}-symmetric vertex model under two assumptions that none of the diagonal elements is constantly zero and that there is at least a pair of elements K^{a}_{b}(z)K^{b}_{a}(z)≠ 0 We make explicit the matrix elements of K(z), parameters they have and the relations among parameters.

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**YOUNG Charles **
* Quantum affine algebras and loop-weight algebras
*

Quantum affine algebras have been the topic of much research over the last 25 or so years. However, even in the category of their finite-dimensional representations, many problems remain open. I will briefly discuss some of these: classifying the prime objects, understanding possible extensions, and even elementary questions like computing dimensions of irreducibles. Then I want to suggest a new approach, which builds on the notion, due to Frenkel and Reshetikhin, of q-characters. The key idea is that, in analogy with the weight lattice of simple Lie algebras, quantum affine algebras have a notion of "loop-weights" and "loop-roots". The analogy with usual weight theory, however, breaks down after a certain point. I shall argue that it is possible to overcome this problem, by obtaining representations as pullbacks of representations of a new algebra, to be defined. Based in part on recent joint work with Evgeny Mukhin, Vyjayanthi Chari and Adriano Moura: arXiv:1206.6657, arxiv:1204.2769 and arxiv:1112.6376

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