ODE/IM correspondence and supersymmetric affine Toda field equations

Affine Toda Field Theory

We present one loop boundary reflection matrix for d (1) 4 Toda field theory defined on a half line with the Neumann boundary condition. This result demonstrates a nontrivial cancellation of non-meromorphic terms which are present when the model has a particle spectrum with more than one mass. Using this result, we determine uniquely the exact boundary reflection matrix which turns out to be ‘n...

Solutions of Discretized Affine Toda Field Equations for A

Solutions of Discretized Affine Toda Field Equations for A

It is known that a family of transfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix of a simple Lie algebra. We formally replace this Cartan matrix of a simple Lie algebra with that of an affine Lie algebra, and then we obtain a system of functional equations different from the T-system. It may be viewed as an X (a) n type affine Toda field eq...

Supersymmetric Yang-mills Theories and Toda Equations

The Solutions of Affine and Conformal Affine Toda Field Theories

We give new formulations of the solutions of the field equations of the affine Toda and conformal affine Toda theories on a cylinder and two-dimensional Minkowski space-time. These solutions are parameterised in terms of initial data and the resulting covariant phase spaces are diffeomorphic to the Hamiltonian ones. We derive the fundamental Poisson brackets of the parameters of the solutions a...