Novel aspects of integrability for NLSMs in symmetric spaces

Abstract

We obtained the formal solution of the auxiliary system of Non Linear Sigma Models, whose target space is a rank 1 symmetric space based on the indefinite orthogonal group O(p,q), corresponding to an arbitrary solution of the NLSM. This class includes Anti-de Sitter, de Sitter and Hyperbolic spaces, which are of interest in view of the AdS/CFT correspondence. The formal solution is related to the Pohlmeyer reduction of the NLSM, constituting another link between the NLSM and the reduced theory. Besides deriving the solution, we also review the Pohlmeyer reduction of such models. Finally, we comment on the implications for the monodromy matrix and its eigenvalues.

arXiv comment38 pages, v2: added section on the conserved charges generated by the monodromy matrix, matches published version

References in corpus (91)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Wilson loops in large N field theories
• Aspects of Holographic Entanglement Entropy
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Review of AdS/CFT Integrability: An Overview
• Gluon scattering amplitudes at strong coupling
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• Classical/quantum integrability in AdS/CFT
• Giant Magnons
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Comments on gluon scattering amplitudes via AdS/CFT
• On classical q-deformations of integrable sigma-models
• Localization techniques in quantum field theories
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• Thermodynamic Bubble Ansatz
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• Matching Higher Conserved Charges for Strings and Spins
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Integrability of the bi-Yang-Baxter sigma-model
• Supersymmetric Wilson loops
• Dyonic Giant Magnons
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Integrable Deformations of Strings on Symmetric Spaces
• Classical/quantum integrability in non-compact sector of AdS/CFT
• The Symmetric Space and Homogeneous sine-Gordon Theories
• The AdS4/CFT3 algebraic curve
• Generating AdS String Solutions
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• More supersymmetric Wilson loops
• On the Dynamics of Finite-Gap Solutions in Classical String Theory
• Lagrangian Formulation of Symmetric Space sine-Gordon Models
• Pohlmeyer reduction revisited
• Single spike solutions for strings on S2 and S3
• Integrable Deformations of Sigma Models
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• A Perspective on Classical Strings from Complex Sine-Gordon Solitons
• On reduced models for superstrings on AdS_n x S^n
• Solitons and AdS String Solutions
• Sinh-Gordon, Cosh-Gordon and Liouville Equations for Strings and Multi-Strings in Constant Curvature Spacetimes
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• Deformed Coset Models From Gauged WZW Actions
• Notes on Euclidean Wilson loops and Riemann Theta functions
• Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve
• Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• Massive Integrable Soliton Theories
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory
• Large Winding Sector of AdS/CFT
• Duality in Complex sine-Gordon Theory
• Wilson loops and minimal area surfaces in hyperbolic space
• On the perturbative S-matrix of generalized sine-Gordon models
• On spacelike and timelike minimal surfaces in $Ad{S}_n$
• Wilson loops and Riemann theta functions II
• Space-like minimal surfaces in AdS x S
• A note on the reduction of the AdS4 x CP3 string sigma model
• Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction
• Brief lectures on duality, integrability and deformations
• Some comments on spacelike minimal surfaces with null polygonal boundaries in $Ad{S}_m$
• Universal aspects of string propagation on curved backgrounds
• Worldsheet Supersymmetry of Pohlmeyer-Reduced AdS_n x S^n Superstrings
• Minimal surfaces in AdS space and Integrable systems
• Series Solution and Minimal Surfaces in AdS
• On Elliptic String Solutions in AdS(3) and dS(3)
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction
• Two-loop corrections to partition function of Pohlmeyer-reduced theory for AdS_5 x S^5 superstring
• Minimal area surfaces in AdS_{n+1} and Wilson loops
• Towards Lefschetz thimbles in Sigma models, I
• Static Elliptic Minimal Surfaces in AdS(4)
• Dressed Elliptic String Solutions on RxS^2
• Stability Analysis of Classical String Solutions and the Dressing Method
• Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S${}^2$
• Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
• Pohlmeyer reduction for superstrings in AdS space
• Fermionic reductions of the AdS4 x CP3 superstring
• The Dressing Method as Non Linear Superposition in Sigma Models
• Dressed Minimal Surfaces in AdS${}_4$
• Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model