Atiyah-Manton Approach to Skyrmion Matter

Abstract

We propose how to approach, and report on the first results in our effort for, describing nuclear matter starting from the solitonic picture of baryons which is supposed to represent QCD for large number of colors. For this purpose, the instanton-skyrmion connection of Atiyah and Manton is exploited to describe skyrmion matter. We first modify 't Hooft's multi-instanton solution so as to suitably incorporate proper dynamical variables into the skyrmion matter and then by taking these variables as variational parameters, we show that they cover a configuration space sufficient to adequately describe the ground state properties of nuclear matter starting from the skyrmion picture. Our results turn out to be comparable to those so far found in different numerical calculations, with our solution reaching stability at high density for a crystal structure and obtaining a comparable value for the energy per baryon at the minimum, thus setting the stage for the next step.

References in corpus (13)

• Continuity of Quark and Hadron Matter
• Rational Maps, Monopoles and Skyrmions
• From Kaon-Nuclear Interactions to Kaon Condensation
• From Chiral Mean Field to Walecka Mean Field and Kaon Condensation
• Attractive Channel Skyrmions and the Deuteron
• Dense Nuclear Matter: Landau Fermi-Liquid Theory and Chiral Lagrangian with Scaling
• A Skyrme lattice with hexagonal symmetry
• Quantising the B=2 and B=3 Skyrmion systems
• Skyrme Crystal from a Twisted Instanton on a Four-Torus
• Nucleons at Finite Temperature
• The kinetic energy and and the geometric structure in the $B=2$ sector of the Skyrme model: A study using the Atiyah-Manton Ansatz
• Quark description of nuclear matter
• The nucleus as a fluid of skyrmions: Energy levels and nucleon properties in the medium

Cited by in corpus (21)

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• Half-Skyrmions and the Equation of State for Compact-Star Matter
• Kaons in Dense Half-Skyrmion Matter
• The Inhomogeneous Phase of Dense Skyrmion Matter
• Baryon chemical potential and in-medium properties of BPS skyrmions
• Enhancement of quark number susceptibility with an alternative pattern of chiral symmetry breaking in dense matter
• Dense matter equation of state and phase transitions from a Generalized Skyrme model
• The half-skyrmion phase in a chiral-quark model
• Introduction to low-momentum effective interactions with Brown-Rho scaling and three-nucleon forces
• Flavor Symmetry and Topology Change in Nuclear Symmetry Energy for Compact Stars
• Constrained instantons and kink-antikink collisions
• Cold Compressed Baryonic Matter with Hidden Local Symmetry and Holography
• Core polarization, Brown-Rho scaling and a memory of Gerry's Princeton years
• Is there a crystalline state of nuclear matter?
• Constrained instanton approximation of Skyrmions with massive pions
• Unified Approach to Dense Matter
• Quantization of the chiral soliton in medium
• Mapping topology of skyrmions and fractional quantum Hall droplets to nuclear EFT for ultra-dense baryonic matter