Topological energy bounds in generalized Skyrme models

Abstract

The Skyrme model has a natural generalization amenable to a standard hamiltonian treatment, consisting of the standard sigma model and the Skyrme terms, a potential, and a certain term sextic in first derivatives. Here we demonstrate that, in this theory, each pair of terms in the static energy functional which may support topological solitons according to the Derrick criterion (i.e., each pair of terms with opposite Derrick scaling) separately posesses a topological energy bound. As a consequence, there exists a four-parameter family of topological bounds for the full generalized Skyrme model. The optimal bounds, i.e., the optimal values of the parameters, depend both on the form of the potential and on the relative strength of the different terms. It also follows that various submodels of the generalized Skyrme model have one-parameter families of topological energy bounds. We also consider the case of topological bounds for the generalized Skyrme model on a compact base space as well as generalizations to higher dimensions.

Latex, 26 pages, version accepted for publication in PRD, presentation and motivation slightly changed, references added, results unchanged

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• Classically isospinning Skyrmion solutions
• Exploring the generalized loosely bound Skyrme model
• Realistic classical binding energies in the $\omega$-Skyrme model
• The Dielectric Skyrme model
• Skyrme crystals, nuclear matter and compact stars
• A Smörgåsbord of Skyrmions
• Baby Skyrme models without a potential term
• Dense matter equation of state and phase transitions from a Generalized Skyrme model
• Crystal structures in generalized Skyrme model
• Bogomolny equation for the BPS Skyrme model from the strong necessary conditions
• Dielectric Skyrmions
• From soft Dirac monopoles to the Dirac equation
• Solitons in the Gauged Skyrme-Maxwell Model
• Vacuum Decay Induced by False Skyrmions
• Near-BPS Skyrmions
• Backreacted Coulomb energy in the Skyrme model
• Nonlinear rigid-body quantization of Skyrmions
• Incompressible topological solitons
• Compressibility of dense nuclear matter in the $\rho$-meson variant of the Skyrme model
• Numerical Evaluation of a Soliton Pair with Long Range Interaction
• Calorons, monopoles and stable, charged solitons
• Maxwell-Higgs self-dual solitons on an infinite cylinder