E. Corrigan

Affine Toda field theory and exact S-matrices

Abstract The masses and three-point couplings for all affine Toda theories are calculated. The exact factorisable S-matrices are conjectured on the basis of the classical masses and couplings and found, in the case of theories based on simply-laced algebras, to give consistent solutions to the bootstrap. An investigation of the properties of the exact S-matrices in perturbation theory is begun but non-perturbative methods will be required to understand the conjectured duality between weak and strong coupling which appears to be a striking feature of these theories.

First-order equations for gauge fields in spaces of dimension greater than four

Abstract We consider the possibility of satisfying the gauge field equations in dimensions greater than four by imposing linear relations amongst the components of the field strength tensor, F μν , generalising the idea of self-duality in four dimensions.

Classically integrable boundary conditions for affine Toda field theories

Abstract Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory.

Affine Toda field theory on a half-line

Abstract The question of the integrability of real-coupling affine toda field theory on a half-line is addressed. It is found, by examining low-spin conserved charges, that the boundary conditions preserving integrability are strongly constrained. In particular, for the a n ( n >1) series of models there can be no free parameters introduced by the boundary condition; indeed the only remaining freedom (apart from choosing the simple condition ∂ 1 φ =0, resides in a choice of signs. For a special case of the boundary condition, it is argued that the classical boundary bound state spectrum is closely related to a consistent set of reflection factors in the quantum field theory.

Scalar field theory and exact solutions to a classical SU (2) gauge theory

We demonstrate a relationship between the solutions of a φ4 scalar field theory and a class of solutions to an SU (2) gauge theory. Most known exact solutions belong to this class.

Ann monopole solution with 4n — 1 degrees of freedom

An exact static monopole solution, possessingn units of magnetic charge and (4n-1) degrees of freedom, is constructed, generalising the recent work of Ward on two monopole solutions. The equations solved are those of anSU(2) gauge theory with adjoint representation Higgs field in the (BPS) limit of vanishing Higgs potential. The number of degrees of freedom is maximal for self-dual solutions. The construction is described in a deductive way, within the framework of the Atiyah-Ward formalism for self-dual gauge fields.

CLASSICALLY INTEGRABLE FIELD THEORIES WITH DEFECTS

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single real scalar fields in each domain and it is found that these may be free, of Liouville type, or of sinh-Gordon type.

Fermion-meson vertices in dual theories

SummaryWe construct the general dual vertex describing the transition of a Ramond fermion into a Neveu-Schwarz meson by the emission of a general excited fermion state. Our vertex thus generalizes the previous results of Thorn and Schwarz and is now put into a relatively compact and manageable form which enables us to check that certain of the general gauge conditions are correctly converted between the meson and fermion legs by the vertex. The particular construction of the vertex can be applied to the other older dual theories and leads to some new insights into them.RiassuntoSi costruise il vertice duale generico che descrive la transizione da un fermione di Ramond ad un mesone di Neveu-Schwarz con l’emissione di uno stato fermionico eccitato generico. Il nostro vertice generalizza così i risultati precedenti di Thorn e Schwarz ed è ora posto in una forma relativamente compatta e maneggevole che ci permette di controllare che alcune delle condizioni di gauge generiche sono convertite correttamente tra le estremità mesoniche e fermioniche del vertice. Questa particolare costruzione del vertice si può applicare ad altre vecchie teorie duali e porta ad alcune nuove visioni di esse.РеэюмеМы конструируем обшую дуальную верщину, описываюшую переход Рамонд-фермиона в меэон Невью-Щварца в реэультате испускания обычного воэбужденного фермионного состояния. Таким обраэом, наща верщина обобшает предыдушие реэультаты Торна и Щварца и дает относительно компактную и податливую форму, которая поэволяет нам проверить, что некоторые обшие калибровочные условия правильно преобраэуются между меэонной и фермионной линиями в рассматриваемой верщине. Специальное конструирование такой верщины может быть применено к другим более старым дуальным теориям и приводит к некоторому более глубокому их пониманию.

Extended Toda Field Theory and Exact S Matrices

Abstract The existence of exact unitary crossing symmetric S -matrices associated with the a, d, e series of Toda field theories is conjectured and the main features illustrated within a discussion of the d 4 case.

Affine Toda field theories with defects

A lagrangian approach is proposed and developed to study defects within affine Toda field theories. In particular, a suitable Lax pair is constructed together with examples of conserved charges. It is found that only those models based on ar(1) data appear to allow defects preserving integrability. Surprisingly, despite the explicit breaking of Lorentz and translation invariance, modified forms of both energy and momentum are conserved. Some, but apparently not all, of the higher spin conserved charges are also preserved after the addition of contributions from the defect. This fact is illustrated by noting how defects may preserve a modified form of just one of the spin 2 or spin -2 charges but not both of them.