Niall MacKay

INTRODUCTION TO YANGIAN SYMMETRY IN INTEGRABLE FIELD THEORY

An introduction to Yangians and their representations, to Yangian symmetry in 1+1D integrable (bulk) field theory, and to the effect of a boundary on this symmetry.

Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line

Abstract: We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by non-local charges. The paper also develops a general framework for obtaining solutions of the reflection equation by solving an intertwining property for representations of certain coideal subalgebras of Uq(ĝ).

Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the ‘tensor product graph’ for solutions of the Yang–Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions.

Boundary Scattering, Symmetric Spaces and the Principal Chiral Model on the Half-Line

We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally) symmetric spaces G/H: there is a class of integrable BCs in which the boundary field is restricted to lie in a coset of H; these BCs are parametrized by G/H×G/H; there are rational solutions of the BYBE in the defining representations of all classical G parametrized by G/H; and using these we propose boundary S-matrices for the principal chiral model, parametrized by G/H×G/H, which correspond to our boundary conditions.

AFFINE TODA SOLITONS AND AUTOMORPHISMS OF DYNKIN DIAGRAMS

Using Hirotas method, solitons are constructed for affine Toda field theories based on the simply laced affine algebras. By considering automorphisms of the simply laced Dynkin diagrams, solutions to the remaining algebras, twisted as well as untwisted, are deduced.

Conserved charges and supersymmetry in principal chiral and WZW models

Abstract Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess–Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra modulo its Coxeter number, can be carried out irrespective of the coefficient of the Wess–Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension.

Yangian symmetry of the Y=0 maximal giant graviton

We study the remnants of Yangian symmetry of AdS/CFT magnons reflecting from boundaries with no degrees of freedom. We present the generalized twisted boundary Yangian of open strings ending on boundaries which preserve only a subalgebra

Twisted algebra R-matrices and S-matrices forbn(1) affine Toda solitons and their bound states

\mathfrak{h}

Achiral boundaries and the twisted Yangian of the D5-brane

of the bulk algebra

Scaling of human body mass with height: The body mass index revisited

\mathfrak{g}