A $T\bar T$-like deformation of the Skyrme model and the Heisenberg model of nucleon-nucleon scattering

TL;DR

This paper introduces a $T\bar T$-like deformation of the Skyrme and Heisenberg models to better describe high-energy nucleon scattering, achieving saturation of the Froissart bound and exploring holographic duals.

Contribution

It develops a novel $T\bar T$-like deformation of the Skyrme model, inspired by 1+1D models, to improve high-energy nucleon scattering descriptions and connects it to holographic interpretations.

Findings

Deformed models saturate the Froissart bound.

Classical soliton solutions are derived and analyzed.

Connections to holographic duals are proposed.

Abstract

The Skyrme model, though it admits correctly a wide range of static properties of the nucleon, does not seem to reproduce properly the scattering behavior of nucleons at high energies. In this paper we present a $T\bar T$-like deformation of it, inspired by a 1+1 dimensional model, in which boosted nucleons behave like shock waves. The scattering of the latter saturates the Froissart bound. We start by showing that 1+1 dimensional $T\bar T$ deformations of the free abelian pion action are in fact generalizations of the old Heisenberg model for nucleon-nucleon scattering, yielding the same saturation of the Froissart bound. We then deform the strong coupling limit of the bosonized action of multi-flavor QCD in two dimensions using the $T\bar T$ deformation of the WZW action with a mass term. We derive the classical soliton solution that corresponds to the nucleon, determine its mass and discuss its transformation into a shock-wave upon boosting. We uplift this action into a 3+1 dimensional $T\bar T$-like deformation of the Skyrme action. We compare this deformed action to that of chiral perturbation theory. A possible holographic gravity dual interpretation is explored.