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

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.

48 pages, no figures; reference added

References in corpus (9)

• Causality, Analyticity and an IR Obstruction to UV Completion
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Introduction to Chiral Perturbation Theory
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• $T\bar{T}$-like Flows in Non-linear Electrodynamic Theories and S-duality
• A Non-Abelian Analogue of DBI from $T\overline{T}$
• AdS-CFT and the RHIC fireball
• Soliton, breather and shockwave solutions of the Heisenberg and the $T\bar{T}$ deformations of scalar field theories in 1+1 dimensions

Cited by in corpus (1)

• $T\bar{T}$ deformations and the pp wave correspondence