Novel aspects of integrability for nonlinear sigma models in symmetric spaces

@article{Katsinis2022NovelAO,
  title={Novel aspects of integrability for nonlinear sigma models in symmetric spaces},
  author={Dimitrios Katsinis},
  journal={Physical Review D},
  year={2022}
}
  • D. Katsinis
  • Published 25 January 2022
  • Mathematics
  • Physical Review D
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… 
1 Citations

Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model

We show that the integrability of the SO ( N ) /SO ( N − 1) Principal Chiral Model (PCM) originates from the Pohlmeyer reduction of the O ( N ) Non Linear Sigma Model (NLSM). In particular, we show

References

SHOWING 1-10 OF 113 REFERENCES

Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model

We show that the integrability of the SO ( N ) /SO ( N − 1) Principal Chiral Model (PCM) originates from the Pohlmeyer reduction of the O ( N ) Non Linear Sigma Model (NLSM). In particular, we show

MORE ABOUT NON-LINEAR SIGMA MODELS ON SYMMETRIC SPACES

Bäcklund transformations for nonlinear sigma models with values in Riemannian symmetric spaces

This work deals with Bäcklund transformations for the principal SL(n, ℂ) sigma model together with all reduced models with values in Riemannian symmetric spaces. First, the dressing method of

Integrable deformations of sigma models

  • B. Hoare
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
In this pedagogical review we introduce systematic approaches to deforming integrable two-dimensional sigma models. We use the integrable principal chiral model and the conformal Wess–Zumino–Witten

Classical/quantum integrability in AdS/CFT

We discuss the AdS/CFT duality from the perspective of integrable systems and establish a direct relationship between the dimension of single trace local operators composed of two types of scalar

On the Dynamics of Finite-Gap Solutions in Classical String Theory

We study the dynamics of finite-gap solutions in classical string theory on R × S 3 . Each solution is characterised by a spectral curve, �, of genus g and a divisor, γ, of degree g on the curve. We

Classical/quantum integrability in non-compact sector of AdS/CFT

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of

Integrable deformations of strings on symmetric spaces

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

Pohlmeyer reduction revisited

A systematic group theoretical formulation of the Pohlmeyer reduction is presented. It provides a map between the equations of motion of sigma models with target-space a symmetric space = F/G and a
...