Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit

TL;DR

This paper constructs an effective field theory for a three-parameter deformed $ ext{AdS}_3 imes S^3 imes T^4$ background in the Landau-Lifshitz limit, analyzing excitation spectra and scattering matrices.

Contribution

It introduces a novel effective field theory for the deformed background and computes the complete perturbative S-matrix in the Landau-Lifshitz approximation.

Findings

Derived the dispersion relation for excitations around the BMN vacuum.

Calculated the perturbative S-matrix including all loop contributions.

Provided insights into the integrable structure of the deformed background.

Abstract

In this article we construct the effective field theory associated to the $\mathbb{R}\times S^3$ sector of the three-parameter deformation of $AdS_3 \times S^3 \times T^4$ in the Landau-Lifshitz approximation. We use this action to compute the dispersion relation of excitations around the BMN vacuum and the perturbative $S$-matrix associated to them. We are able to compute and sum all the different loop contributions to the $S$-matrix in this limit.