Yang–Baxter Deformation of 2D Non-Linear Sigma Models: Towards Applications to AdS/CFT

Preface
Acknowledgements
Contents
1 Integrable Non-linear Sigma Models in (1+1)-Dimensions
	1.1 What is Classical Integrability?
	1.2 Principal Chiral Model
		1.2.1 Classical Action and Symmetry
		1.2.2 Target-Space Geometry
		1.2.3 BIZZ Construction of Non-local Conserved Charges
		1.2.4 Yangian Algebra
		1.2.5 Lax Pair and Monodromy Matrix
	1.3 Symmetric Coset Sigma Model
		1.3.1 Symmetric Coset
		1.3.2 Classical Action and Symmetry
		1.3.3 The Proof of the Flatness Condition
		1.3.4 Example: Coset Construction of S2
		1.3.5 Another Form of Lax Pair
	References
2 Yang–Baxter Sigma Models
	2.1 Classical Yang–Baxter Equation and Linear R-Operator
	2.2 Yang–Baxter Deformation of 2D Principal Chiral Model
		2.2.1 Deformed Classical Action
	2.3 Yang–Baxter Deformation of Symmetric Coset Model
		2.3.1 Deformed Classical Action
		2.3.2 Lax Pair
	2.4 History of the Development of the Yang–Baxter Deformation
	References
3 Recent Progress on Yang–Baxter Deformation and Generalized Supergravity
	3.1 Introduction
	3.2 Yang–Baxter Deformation of the AdS5timesS5 Superstring
		3.2.1 Classical Integrability of the AdS5timesS5 Superstring
		3.2.2 Yang–Baxter Deformed Action and Supercoset Construction
		3.2.3 Unimodular Examples
	3.3 Generalized Supergravity
		3.3.1 Non-unimodular Example
		3.3.2 Hoare-Tseytlin Conjecture
		3.3.3 Non Yang–Baxter Solution
	3.4 Other Topics
	References