Quantum Nucleationof Topological Solitons
Muneto Ni*a(新田宗土)
Keio U. (慶應義塾大学)

熱場の量子論@ YITP
Sep 21, 2022

Minoru Eto (衛藤稔) 山形大学
JHEP 09 (2022) 077 [2207.00211 [hep-th]]See also Higaki, Kamada, Nishimura, 2207.00212 [hep-th]False vacuum decay
Coleman(‘77)= Quantum nucleation of a bubble
False Vacuum

True
True
VacuumVacuum

True

False

False vacuum decay
Coleman(‘77)= Quantum nucleation of a bubble
False Vacuum
EQuantumtunneling

R0

True R0
Vacuum

True

False

R
Domain wall tension @surface

Topological soliton decay Preskill & Vilenkin(‘93)= Quantum nucleation of a hole𝑬 = −𝝅𝑹𝟐 𝑻𝒘𝒂𝒍𝒍 + 𝟐𝝅𝑹𝑻𝒔𝒕𝒓𝒊𝒏𝒈

DomainwallEholehole

A holebound bya string
loop

Quantumtunneling

R0R

Topological soliton creation Ours (‘22)= Quantum nucleation of a soliton
𝑬 = +𝝅𝑹𝟐 𝑻𝒘𝒂𝒍𝒍 + 𝟐𝝅𝑹𝑻𝒔𝒕𝒓𝒊𝒏𝒈

VacuumPossible if 𝑻𝒘𝒂𝒍𝒍 < 𝟎E
A soliton
diskbound bya string
loop

disk
disk

Quantumtunneling

R0R

Topological soliton creation Ours (‘22)= Quantum nucleation of a soliton
Is it possible?

𝑬 = +𝝅𝑹𝟐 𝑻𝒘𝒂𝒍𝒍 + 𝟐𝝅𝑹𝑻𝒔𝒕𝒓𝒊𝒏𝒈

Possible if 𝑻𝒘𝒂𝒍𝒍 < 𝟎YES!!
Solitonic ground states
1. Chiral soliton lattices in chiral magnets
2. Skyrmion lattices in chiral magnets
3. Chiral soliton lattices in QCD understrong magnetic field Son-Stephanov(’07), Brauner-Yamamoto (‘16)
rapid rotation Huang-Nishimura-Yamamoto(‘17)
Both relevant for QGP
Other situation: de Sitter space Basu-Guth-Vilenkin(‘91)

The model at IR (common for chiral magnets & QCD)
= sine-Gordon model + topological term

CME for magnetic field
CVE for rotation

The UV theory = axion (Goldstone) model + topoFor 𝒎 = 𝟎 (Goldstone model)
Nambu-Goldstone (NG) mode + Higgs mode
Global string
thicknesstension

𝑳: system size (IR cutoff)For 𝒎 ≠ 𝟎, pseudo NG mode
We consider
For simplicity
Sine-Gordon(SG) soliton
thicknesstensionFor finite 𝒎𝒉 ,1) SG soliton is metastable2) SG-soliton can be bound by a string3) String has a finite tension
Missing in
Preskill-VilenkinWithout the topological term,
the decay probability is (Preskill-Vilenkin)C

Nucleation probability with the topological term

𝜶: Angle between soliton and B

2+1 dimThin-defect approx

Numerical simulation in 2+1 dim: relaxation

Stringtension

Decay prob
Consistent withthin-defect approx

3+1 dimThin-defect approx

Numerical simulation in 3+1 dim: relaxation

Nucleation
probability
We found a remnant energy 𝒄giving a correction to the thin-defect approx

Formation of chiral soliton latticeSummary

Topological soliton creation Ours (‘22)= Quantum nucleation of a soliton

M.Eto & MN,JHEP 09 (2022) 077[2207.00211 [hep-th]]Possible if 𝑻𝒘𝒂𝒍𝒍 < 𝟎EVacuumA soliton
diskbound bya stringloop

𝑬 = +𝝅𝑹𝟐 𝑻𝒘𝒂𝒍𝒍 + 𝟐𝝅𝑹𝑻𝒔𝒕𝒓𝒊𝒏𝒈

disk

Quantumtunneling

R0R

Classification of topological solitons: 3 types
𝒅 Defects
Gauge Structure
Textures
1 Domain wall, 𝝅𝟎Sine-Gordon
𝝅𝟏Kinksoliton2Vortex,
Lumps,𝝅𝟏
𝝅𝟐Cosmic string
Baby Skyrmion
3Monopole𝝅𝟐 Skyrmion, Hopfion 𝝅𝟑4YM instanton 𝝅𝟑
𝝏𝑹𝒅 ≅ 𝑺𝒅"𝟏 → 𝑮/𝑯

𝑹𝒅 + {∞} = 𝑺𝒅 → 𝑮/𝑯𝝏𝑹𝒅 ≅ 𝑺𝒅"𝟏 → 𝑮

πd-1 (G/H) ≠ 0

πd (G/H) ≠ 0

πd-1 (G) ≠ 0𝒅: codimensions (in which solitons are particles, or on which solitons depend)

Domain wall (defect)

π0 (Z2) = Z2 ≠ 0

R1Sine-Gordon soliton (texture) π1 (S1) = Z ≠ 0

S1
R1

Vortex, cosmic string (defect) π1 (S1) = Z ≠ 0

stereographicS2

R2

Lump, baby Skyrmion (texture)

π2 (S2) = Z ≠ 0

R2
Notdefect

Monopole (defect)“hedgehog”

π2 (S2) = Z ≠ 0

S 2 = ¶R 3
From Wikipedia

R3

Skyrmion (texture)

π3 (S3) = Z ≠ 0

Notdefect

From Wikipedia

R3

How are they created?
e.g. Kibble-Zurek mechanism @ phase transition

Domain walls