“Half a proton” in the Bogomol’nyiPrasadSommerfield Skyrme model
Abstract
The BPS Skyrme model is a model containing an SU(2)valued scalar field, in which a Bogomol’nyitype 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 pullback 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:
 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’nyiPrasadSommerfield Skyrme model. United States: N. p., 2016.
Web. doi:10.1063/1.4959234.
Lukács, Árpád. “Half a proton” in the Bogomol’nyiPrasadSommerfield Skyrme model. United States. doi:10.1063/1.4959234.
Lukács, Árpád. 2016.
"“Half a proton” in the Bogomol’nyiPrasadSommerfield Skyrme model". United States.
doi:10.1063/1.4959234.
@article{osti_22596591,
title = {“Half a proton” in the Bogomol’nyiPrasadSommerfield Skyrme model},
author = {Lukács, Árpád},
abstractNote = {The BPS Skyrme model is a model containing an SU(2)valued scalar field, in which a Bogomol’nyitype 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 pullback 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 PrasadSommerfield solution for the 't Hooft monopole can be transformed to an exact timedependent solution (which is singular on the light cone) of the SU(2) YangMillsHiggs system.

NonAbelian Bogomol{close_quote}nyiPrasadSommerfield Monopoles in {ital N} =4 Gauged Supergravity
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 BPSmonopoletype gauge field and a globally hyperbolic, everywhere regular geometry. These present the first known example of nonAbelian backgrounds in gauge supergravity and in leading order effective string theory. {copyright} {ital 1997} {ital The American Physical Society} 
Complex Bogomol{close_quote}nyiPrasadSommerfield Domain Walls and Phase Transition in Mass in Supersymmetric QCD
We study the domain walls connecting different chirally asymmetric vacua in supersymmetric QCD. We show that Bogomol{close_quote}nyiPrasadSommerfield (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} 
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