Non-simply Laced Affine Toda Theories Research Articles

Reflection amplitudes in non-simply laced Toda theories and thermodynamic Bethe ansatz

We study the ultraviolet asymptotics in non-simply laced affine Toda theories considering them as perturbed non-affine Toda theories, which possess the extended conformal symmetry. We calculate the reflection amplitudes, in non-affine Toda theories and use them to derive the quantization condition for the vacuum wave function, describing zero-mode dynamics. The solution of this quantization conditions for the ground state energy determines the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with Thermodynamic Bethe Ansatz (TBA) results. To make the comparison with TBA possible, we give the exact relations between parameters of the action and masses of particles as well as the bulk free energies for non-simply laced affine Toda theories.

S-matrices of non-simply laced affine Toda theories by folding

The exact factorisable quantum S-matrices are known for simply laced as well as non-simply laced affine Toda field theories. Non-simply laced theories are obtained from the affine Toda theories based on simply laced algebras by folding the corresponding Dynkin diagrams. The same process, called classical ‘reduction’, provides solutions of a non-simply laced theory from the classical solutions with special symmetries of the parent simply laced theory. In the present note we shall elevate the idea of folding and classical reduction to the quantum level. To support our views we have made some interesting observations for S-matrices of non-simply laced theories and give a prescription for obtaining them through the folding of simply laced ones.

Integrable deformations of affine Toda theories and duality

We introduce and study five series of one-parameter families of two-dimensional integrable quantum field theories. These theories have a Lagrangian description in terms of the massive Thirring model coupled with non-simply laced affine Toda theories. Perturbative calculations, analysis of the factorized scattering theory and the Bethe ansatz technique are used to show that these field theories possess the dual representation available for the perturbative analysis in the strong coupling limit. The dual theory can be formulated as the non-linear sigma model with Witten's Euclidean black hole metric (complex sinh-Gordon theory) coupled with non-simply laced affine Toda theories. Lie algebras associated with these “dual” Toda theories belong to the dual series of affine algebras but have a smaller rank. The exact relation between coupling constants in the dual theories is conjectured.

Monte Carlo study of exact S-matrix duality in nonsimply laced affine Toda theories.

The $(g_2^{(1)}, d_4^{(3)})$\ pair of non simply laced affine Toda theories is studied from the point of view of non perturbative duality. The classical spectrum of each member is composed of two massive scalar particles. The exact S-matrix prediction for the dual behaviour of the coupling dependent mass ratio is found to be in strong agreement with Monte Carlo data.

Quantum boundary currents for nonsimply-laced Toda theories

We study the quantum integrability of nonsimply-laced affine Toda theories defined on the half-plane and explicitly construct the first nontrivial higher-spin charges in specific examples. We find that, in contradistinction to the classical case, addition of total derivative terms to the “bulk” current plays a relevant role for the quantum boundary conservation.

Exact S-matrices for nonsimply-laced affine Toda theories

We derive exact, factorized, purely elastic scattering matrices for the affine Toda theories based on the nonsimply-laced Lie algebras a 2 n−1 (2), b n (1), c c (1), d n (2), and g n (1), as well as the superalgebras A (4)(0, 2 n) and B (1)(0, n).

Exact S-matrices for the nonsimply-laced affine Toda theories a (2)2n−1

We derive the exact, factorized, purely elastic scattering matrices for the a (2) 2n−1 family of nonsimply-laced affine Toda theories. The derivation takes into account the distortion of the classical mass spectrum by radiative corrections, as well as modifications of the usual bootstrap assumptions since for these theories anomalous threshold singularities lead to a displacement of some single particle poles.