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

TL;DR

This paper explores a dual strong coupling description of the integrability-preserving deformation of the $O(N)$ sigma model, showing that the dual theory shares the same integrable structure and coincides as a quantum field theory.

Contribution

It introduces a dual description involving fermionic and bosonic fields that preserves integrability and matches the $ ext{eta}$-deformed $O(N)$ sigma model after T-duality.

Findings

Dual theory shares the same integrable structure as the original.

Constructed a Ricci flow solution matching the $ ext{eta}$-deformed metric.

Showed the dual theory coincides with the deformed sigma model after T-duality.

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 $\eta-$deformed $O(N)$ sigma-model after $T-$duality transformation.