# Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory

@inproceedings{Schmidtt2021SymmetricS, title={Symmetric space \$\lambda\$-model exchange algebra from 4d holomorphic Chern-Simons theory}, author={D. M. Schmidtt}, year={2021} }

We derive, within the Hamiltonian formalism, the classical exchange algebra of a lambda deformed string sigma model in a symmetric space directly from a 4d holomorphic Chern-Simons theory. The explicit forms of the extended Lax connection and R-matrix entering the Maillet bracket of the lambda model are explained from a symmetry principle. This approach, based on a gauge theory, may provide a mechanism for taming the nonultralocality that afflicts most of the integrable string theories… Expand

#### References

SHOWING 1-10 OF 32 REFERENCES

Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles

- Physics
- 2015

We describe a unifying framework for the systematic construction of integrable deformations of integrable σ-models within the Hamiltonian formalism. It applies equally to both the 'Yang–Baxter' type… Expand

The Classical Exchange Algebra of AdS5 x S^5

- Physics
- 2008

The classical exchange algebra satisfied by the monodromy matrix of AdS5× S 5 string theory in the Green-Schwarz formulation is determined by using a first-order Hamiltonian formulation and by adding… Expand

Yang-Baxter $\sigma$-models and dS/AdS T-duality

- Physics
- 2002

We point out the existence of nonlinear $\sigma$-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular… Expand

Integrable lattice models from four-dimensional field theories

- Physics, Mathematics
- 2013

This note gives a general construction of an integrable lattice model (and a solution of the Yang-Baxter equation with spectral parameter) from a four-dimensional field theory which is a mixture of… Expand

Holomorphic Chern-Simons theory and affine Gaudin models

- Physics, Mathematics
- 2019

We relate two formalisms recently proposed for describing classical integrable field theories. The first is based on the action of four-dimensional holomorphic Chern-Simons theory introduced and… Expand

S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models

- Physics
- 2015

Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the… Expand

Supersymmetric gauge theory and the Yangian

- Physics, Mathematics
- 2013

This paper develops a new connection between supersymmetric gauge theories and the Yangian. I show that a twisted, deformed version of the pure N=1 supersymmetric gauge theory is controlled by the… Expand

New integrable canonical structures in two-dimensional models

- Physics
- 1986

Abstract We develop a new canonical r - s matrix type approach for integrable two-dimensional models of non-ultralocal type. The L -matrices algebra and the monodromy matrices' algebras are given in… Expand

Integrable Lattice Models From Gauge Theory

- Physics
- 2016

These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge… Expand

Integrable deformations of strings on symmetric spaces

- Physics
- 2014

A bstractA general class of deformations of integrable sigma-models with symmetric space F/G target-spaces are found. These deformations involve defining the non-abelian T dual of the sigma-model and… Expand