Related papers: Aspects of 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.
This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT-symmetric quantum mechanics are discussed, and some…
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…
Recently, a remarkable correspondence has been unveiled between a certain class of ordinary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerning the 2nd order…
We study the quantum spectral curve of the Argyres-Douglas theories in the Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM correspondence we investigate the quantum integrable model corresponding to the quantum spectral…
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 spectral correspondence between a particular class of Schrodinger equations and supersymmetric quantum integrable model (QIM). The latter, a quantized version of the Ablowitz-Kaupp-Newell-Segur (AKNS) hierarchy of nonlinear…
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.
We study the linear differential system associated with the supersymmetric affine Toda field equations for affine Lie superalgebras, which has a purely odd simple root system. For an affine Lie algebra, the linear problem modified by…
The Fateev model is somewhat special among two-dimensional quantum field theories. For different values of the parameters,it can be reduced to a variety of integrable systems. An incomplete list of the reductions includes O(3) and O(4)…
We outline a relationship between conformal field theories and spectral problems of ordinary differential equations, and discuss its generalisation to models related to classical Lie algebras.
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…
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…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
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…
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…
Within the framework of the ODE/IM correspondence, we show that the minimal conformal field theories with c<1 emerge naturally from the monodromy properties of certain families of ordinary differential equations.
We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The…
A connection between nuclear symmetries other than those of an ellipsoidal nucleus and the properties of the implied rotational spectra are discussed. The discussion is focussed on a few examples of exotic shapes predicted recently by…