Related papers: The ODE/IM Correspondence
A connection between integrable quantum field theory and the spectral theory of ordinary differential equations is reviewed, with particular emphasis being given to its relevance to certain problems in PT-symmetric quantum mechanics.
We review a surprising correspondence between certain two-dimensional integrable models and the spectral theory of ordinary differential equations. Particular emphasis is given to the relevance of this correspondence to certain problems in…
We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…
This review describes a link between Lax operators, embedded surfaces and Thermodynamic Bethe Ansatz equations for integrable quantum field theories. This surprising connection between classical and quantum models is undoubtedly one of the…
We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.
One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d <= 2…
In this paper the relation between 2d topological gauge theories and Bethe Ansatz equations is reviewed. In addition we present some new results and clarifications. We hope the relations discussed here are particular examples of more…
We explain the relationship between the classical description of an integrable system in terms of invariant tori and action-angle variables, and the quantum description in terms of the asymptotic Bethe ansatz.
The massive ODE/IM correspondence is a relation between the linear problem associated with modified affine Toda field equations and two-dimensional massive integrable models. We study the massive ODE/IM correspondence for the…
We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe…
This review was born as notes for a lecture given at the YRIS school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov…
The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…
The term Bethe Ansatz stands for a multitude of methods in the theory of integrable models in statistical mechanics and quantum field theory that were designed to study the spectra, the thermodynamic properties and the correlation functions…
Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model…
This is a brief review of my work on the correspondence between four-dimensional $\mathcal{N} = 1$ supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
We conjecture the factorized scattering description for OSP(m/2n)/OSP(m-1/2n) supersphere sigma models and OSP(m/2n) Gross Neveu models. The non-unitarity of these field theories translates into a lack of `physical unitarity' of the S…
We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral…
We study the ODE/IM correspondence for ODE associated to $\hat{\mathfrak g}$-valued connections, for a simply-laced Lie algebra $\mathfrak g$. We prove that subdominant solutions to the ODE defined in different fundamental representations…
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…