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Title: “Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model

Abstract

The BPS Skyrme model is a model containing an SU(2)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU(2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here that in the BPS Skyrme model such solutions exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.

Authors:
 [1]
  1. MTA Wigner RCP, RMI, P.O. Box 49, Budapest H1525 (Hungary)
Publication Date:
OSTI Identifier:
22596591
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL SOLUTIONS; SCALAR FIELDS; SOLITONS; SYMMETRY; TOPOLOGY

Citation Formats

Lukács, Árpád. “Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model. United States: N. p., 2016. Web. doi:10.1063/1.4959234.
Lukács, Árpád. “Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model. United States. doi:10.1063/1.4959234.
Lukács, Árpád. 2016. "“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model". United States. doi:10.1063/1.4959234.
@article{osti_22596591,
title = {“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model},
author = {Lukács, Árpád},
abstractNote = {The BPS Skyrme model is a model containing an SU(2)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU(2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here that in the BPS Skyrme model such solutions exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.},
doi = {10.1063/1.4959234},
journal = {Journal of Mathematical Physics},
number = 7,
volume = 57,
place = {United States},
year = 2016,
month = 7
}
  • We show that the Prasad-Sommerfield solution for the 't Hooft monopole can be transformed to an exact time-dependent solution (which is singular on the light cone) of the SU(2) Yang-Mills-Higgs system.
  • We study static, spherically symmetric, and purely magnetic solutions of SU(2){times}SU(2) gauge supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/4 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. These present the first known example of non-Abelian backgrounds in gauge supergravity and in leading order effective string theory. {copyright} {ital 1997} {ital The American Physical Society}
  • We study the domain walls connecting different chirally asymmetric vacua in supersymmetric QCD. We show that Bogomol{close_quote}nyi-Prasad-Sommerfield (BPS) saturated solutions exist only in the limited range of mass m{le}m{sub {asterisk}}{approx}0.8{vert_bar}{l_angle}Tr {lambda}{sup 2}{r_angle}{vert_bar}{sup 1/3} . When m{gt}m{sub {asterisk}} , the domain wall either ceases to be BPS saturated or disappears altogether. In any case, the properties of the system are qualitatively changed. {copyright} {ital 1997} {ital The American Physical Society}
  • A variational search for multimonopole solutions of the Yang-Mills-Higgs equations in the Prasad-Sommerfield limit is performed. An ansatz where two monopoles are superimposed at the origin is shown to lead to a minimal energy differing by less than one percent from the Bogomolny bound, with the discrepancy attributable to the truncation error. Thus strong numerical evidence is obtained for the existence of two-monopole solutions, the symmetry properties of which are discussed.
  • It is shown that the Bogomolny equations for the simplest static, axially symmetric gauge fields are equivalent to the ernst equation. The Bogolmolny-Prasad-Sommerfield one-monopole solution is obtained via Harrison's Baecklund transformation.