# INTRODUCTION TO YANGIAN SYMMETRY IN INTEGRABLE FIELD THEORY

@article{Mackay2004INTRODUCTIONTY, title={INTRODUCTION TO YANGIAN SYMMETRY IN INTEGRABLE FIELD THEORY}, author={Niall J. Mackay}, journal={International Journal of Modern Physics A}, year={2004}, volume={20}, pages={7189-7217} }

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.

## 132 Citations

Twisted Yangian symmetry of the open Hubbard model

- Physics, Mathematics
- 2014

We show that, in the open Hubbard model with integrable boundary conditions, the bulk Yangian symmetry is broken to a twisted Yangian. We prove that the associated charges commute with the…

An integrability primer for the gauge-gravity correspondence: an introduction

- Physics
- 2016

We introduce a series of articles reviewing various aspects of integrable models relevant to the anti-de Sitter (AdS)/conformal quantum field theory (CFT) correspondence. Topics covered in these re…

Review of AdS/CFT Integrability. Chapter VI.2: Yangian Algebra

- Mathematics
- 2010

We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of integrability for the $${\mathcal{N} = 4}$$…

Yangian symmetry of boundary scattering in AdS/CFT and the explicit form of bound state reflection matrices

- Mathematics
- 2011

The reflection matrices of multi magnon bound states are obtained explicitely by exploiting the Yangian symmetry of boundary scattering on the Y = 0 maximal giant graviton brane.

From Twisted Quantum Loop Algebras to Twisted Yangians

- Mathematics
- 2015

We prove how the Yangian of glN in its RTT presentation and Olshanski's twisted Yangians for the orthogonal and symplectic Lie algebras can be obtained by a de- generation process from the…

Reflection algebra, Yangian symmetry and bound-states in AdS/CFT

- Mathematics
- 2012

A bstractWe present the ‘Heisenberg picture’ of the reflection algebra by explicitly constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends on a boundary with non-trivial…

The secret symmetries of the AdS/CFT reflection matrices

- Mathematics
- 2011

We find new twisted Yangian symmetries of the AdS/CFT reflection matrices for the Y=0 maximal giant graviton and D5-brane. These new symmetries originate from the known secret symmetries of the…

Secret symmetries in AdS/CFT

- Physics
- 2012

We discuss special quantum group (secret) symmetries of the integrable system associated with the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including…

Achiral boundaries and the twisted Yangian of the D5-brane

- Mathematics
- 2011

We consider integrable field theories with achiral boundary conditions and uncover the underlying achiral twisted Yangian algebra. This construction arises from old work on the bosonic principal…

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