Related papers: The Toda-Weyl mass spectrum
Many integrable theories can be formulated universally in terms of Lie algebraic root systems. Well-studied are conformally invariant scalar field theories of Toda type and their massive versions, which can be expressed in terms of simple…
A cross between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system, is introduced for any affine root system. Though it is not completely integrable but partially integrable, or quasi exactly…
The local mass is a fundamental quantized information that characterizes the blow-up solution to the Toda system and has a profound relationship with its underlying algebraic structure. In \cite{Lin-Yang-Zhong-2020}, it was observed that…
In this article we obtain total masses of solutions to the Toda system associated to a general simple Lie algebra with singular sources at the origin. The determination of such total masses is one of the important steps towards establishing…
It has been established that the local mass of blow-up solutions to Toda systems associated with the simple Lie algebras $\mathbf{A}_n,~\mathbf{B}_n,~\mathbf{C}_n$ and $\mathbf{G}_2$ can be represented by a finite Weyl group. In particular,…
The spectra of $A_r$ affine Toda field theories with imaginary coupling constant, are investigated. Soliton solutions are found, which, despite the non-unitary form of the Lagrangian, have real classical masses and are stable to small…
We present a definition of the non-abelian generalisations of affine Toda theory related from the outset to vertex operator constructions of the corresponding Kac-Moody algebra $\gh$. Reuslts concerning conjugacy classes of the Weyl group…
We propose affine Toda field theories related to the non-crystallographic Coxeter groups H_2, H_3 and H_4. The classical mass spectrum, the classical three-point couplings and the one-loop corrections to the mass renormalisation are…
We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple…
We study the conserved charges of affine Toda field theories by making use of the conformally invariant extension of these theories. We compute the values of all charges for the single soliton solutions, and show that these are related to…
We calculate the first quantum corrections to the masses of solitons in imaginary-coupling affine Toda theories using the semi-classical method of Dashen, Hasslacher and Neveu. The theories divide naturally into those based on the…
Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras $A_2$, $B_2$, $C_2$, $G_2$ the complete sets…
The most prominent class of integrable quantum field theories in 1+1 dimensions is affine Toda theory. Distinguished by a rich underlying Lie algebraic structure these models have in recent years attracted much attention not only as test…
Using a contraction procedure, we obtain Toda theories and their structures, from affine Toda theories and their corresponding structures. By structures, we mean the equation of motion, the classical Lax pair, the boundary term for half…
An analysis is given of the structure of a general two-dimensional Toda field theory involving bosons and fermions which is defined in terms of a set of simple roots for a Lie superalgebra. It is shown that a simple root system for a…
We propose new models of an `affine' theory of gravity in $D$-dimensional space-times with symmetric connections. They are based on ideas of Weyl, Eddington and Einstein and, in particular, on Einstein's proposal to specify the space - time…
We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine $sl(3)^{(1)}$ Toda model coupled to matter fields (CATM). The theory is treated as a constrained system in the context of…
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge…
We show that Toda lattices with the exceptional Cartan matrices are Liouville type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants.
We note that S-matrix/conserved charge identities in affine Toda field theories of the type recently noted by Khastgir can be put on a more systematic footing. This makes use of a result first found by Ravanini, Tateo and Valleriani for…