**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)/Z_{3}
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.