Non-Abelian vortex in lattice gauge theory
Arata Yamamoto (U. Tokyo)
AY, PTEP 2018, 103B03 (2018)
condensed matter QCD
superconductors neutron stars
Introduction
https://en.wikipedia.org/wiki/Magnetar Wells, Pan, Wang, Fedoseev, Hilgenkamp (2015)
Introduction
condensed matter QCD
SU(3)C-F×U(1)/Z3 color-flavor locking condensation
U(1)
Cooper pair of electrons
“diquark”
Cooper pair of quarks
e e q q q q q q
Introduction
condensed matter QCD
Abelian vortex non-Abelian vortex
Introduction
condensed matter QCD
Abelian vortex non-Abelian vortex
e.g.
semi-classical level full-quantum level
mean-field analysis lattice gauge theory
http://jcahpc.jp/pr/pr-20171115.html
Introduction
Setup
discretize Setup
discretize
Monte Carlo Setup
Setup
non-Abelian Higgs model
:SU(3)F×SU(3)C×U(1) scalar field :dynamical SU(3)C gauge field
:external U(1) gauge field
Setup
non-Abelian Higgs model
:SU(3)F×SU(3)C×U(1) scalar field :dynamical SU(3)C gauge field
:external U(1) gauge field
SU(3)C field strength
SU(3)C×U(1) covariant derivative
scalar field potential
Setup
non-Abelian Higgs model
:anti-triplet diquarks :dynamical gluons
:external magnetic field in neutron stars
SU(3)C×U(1) covariant derivative
scalar field potential SU(3)C field strength
non-Abelian vortex condensate
color-flavor locking
magnetic field
Phase structure
Phase structure
Phase structure
U(1)
condensate
?
gauge dependent
Phase structure
condensate
U(1)
Phase structure
condensate
U(1)
Phase structure
condensate
U(1)
condensed &
deconfined phase
Phase structure
U(1)
Phase structure
color-flavor locking
SU(3)C-F
flavor color
U(1)
Phase structure
color-flavor locking
SU(3)C-F U(1)
Phase structure
color-flavor locking
SU(3)C-F U(1)
off-diagonal / diagonal
Phase structure
color-flavor locking
SU(3)C-F U(1)
color-flavor locked phase
off-diagonal / diagonal
non-Abelian vortex condensate
color-flavor locking
magnetic field Non-Abelian vortex
Non-Abelian vortex
? phase variable
gauge dependent
Non-Abelian vortex
phase variable Alford, Baym, Fukushima, Hatsuda, Tachibana (2018)
Non-Abelian vortex phase variable
vortex number density magnetic field
q
Alford, Baym, Fukushima, Hatsuda, Tachibana (2018)
Non-Abelian vortex
vortex number density condensate
Non-Abelian vortex
vortex number density condensate
Monte Carlo
Non-Abelian vortex
Q = 0
Q =1/3
Non-Abelian vortex
Non-Abelian vortex
Non-Abelian vortex
Non-Abelian vortex
Non-Abelian vortex
Non-Abelian vortex
vortex-vortex interaction is repulsive
decay
one Abelian vortex three non-Abelian vortices
Nakano, Nitta, Matsuura (2008) Alford, Mallavarapu, Vachaspati, Windisch (2016)
cf. mean-field analysis
Summary
used gauge-invariant operators
obtained color-flavor locked phase
obtained vortex distributions
ultimate goal: lattice QCD at high density I studied non-Abelian vortices in lattice gauge theory.
