On dual description of the deformed O(N) sigma model

A V Litvinov,L A Spodyneiko

doi:10.1007/jhep11(2018)139

Abstract

We study dual strong coupling description of integrability-preserving deformation of the O(N) sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions. We claim that both theories share the same integrable structure and coincide as quantum field theories. We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the η-deformed O(N) sigma-model after T -duality transformation.

Highlights

Perturbative regime of the Toda-Thirring model and vice versa
We study dual strong coupling description of integrability-preserving deformation of the O(N ) sigma model
We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the η-deformed O(N ) sigma-model after T -duality transformation

Summary

Dual Lagrangians

Let us start with known results and consider the theory defined by the Lagrangian density (1.21). The last condition is equivalent to the absence of singularity at infinity, which is always the case for correlation functions (3.8) It can be used for computation of many interesting Coulomb integrals appearing in CFT (see for example [28]). We note that the operator Rr is just an application of the integral identity (3.10) to the contribution of the fermionic root αr It changes the roots αs → αs as well as shifts the charges of the exponential fields according to a → a + αr. As explained in [22], the operator Rr can be lifted to the operator, called fermionic reflection operator, acting on the total “off-shell” correlation functions It serves as an isomorphism between different conformal field theories, corresponding to different root systems. See ref. [29] for more details on this model, its dual description and relation to the superalgebra D(2|1, α)

Ricci flow equations

Conclusions

A Integrals of Motion

B Parametrization of the group elements