Real-time Evolution of U ( 1 ) Chiral Charge Daniel Figueroa Adrien - - PowerPoint PPT Presentation

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Real-time Evolution of U ( 1 ) Chiral Charge Daniel Figueroa Adrien - - PowerPoint PPT Presentation

Jan 23, 2024 247 likes •660 views

Real-time Evolution of U ( 1 ) Chiral Charge Daniel Figueroa Adrien Florio Mikhail Shaposhnikov Lattice 2018, 23 th of July 2018 Overview Lattice Model Results/Outlooks Overview Lattice Model Results/Outlooks Anomalous Processes Gauge

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SLIDE 1

Real-time Evolution of U(1) Chiral Charge

Daniel Figueroa Mikhail Shaposhnikov Adrien Florio Lattice 2018, 23th of July 2018

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SLIDE 2

Overview Lattice Model Results/Outlooks

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SLIDE 3

Overview Lattice Model Results/Outlooks

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SLIDE 4

Anomalous Processes

Fermionic charge Anomaly Gauge bosons Baryogenesis Chiral Magnetic Effect Axion Physics

1

  • A. Florio, Lattice2018, 23/07/18
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SLIDE 5

Anomalous Processes

Fermionic charge Anomaly Gauge bosons Baryogenesis Chiral Magnetic Effect Axion Physics U(1)

1

  • A. Florio, Lattice2018, 23/07/18
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SLIDE 6

Anomalous Processes Model

  • A. Florio, Lattice2018, 23/07/18

Fermionic charge Anomaly Gauge bosons Baryogenesis Chiral Magnetic Effect Axion Physics U(1)

  • 1

2

L = − 1

4FµνFµν + ¯

Ψ/ DΨ +(Dµφ)∗Dµφ − V(φ) with: jµ

5 = ¯

Ψγµγ5Ψ V(φ) = m2|φ|2 + λ|φ|4

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SLIDE 7

Anomalous Processes Model

  • A. Florio, Lattice2018, 23/07/18

Fermionic charge Anomaly Gauge bosons Baryogenesis Chiral Magnetic Effect Axion Physics U(1)

  • 1

2

L = − 1

4FµνFµν + ¯

Ψ/ DΨ +(Dµφ)∗Dµφ − V(φ) with: jµ

5 = ¯

Ψγµγ5Ψ V(φ) = m2|φ|2 + λ|φ|4 Anomaly: ∂µjµ

5 = e2 8π2 Fµν ˜

Fµν

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SLIDE 8

Model Abelian Instabilities

  • A. Florio, Lattice2018, 23/07/18

L = − 1

4FµνFµν + ¯

Ψ/ DΨ +(Dµφ)∗Dµφ − V(φ) with: jµ

5 = ¯

Ψγµγ5Ψ V(φ) = m2|φ|2 + λ|φ|4 Anomaly: ∂µjµ

5 = e2 8π2 Fµν ˜

Fµν

  • 2

3

Integrate out Ψ FCS = µNCS

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SLIDE 9

Model Abelian Instabilities

  • A. Florio, Lattice2018, 23/07/18

L = − 1

4FµνFµν + ¯

Ψ/ DΨ +(Dµφ)∗Dµφ − V(φ) with: jµ

5 = ¯

Ψγµγ5Ψ V(φ) = m2|φ|2 + λ|φ|4 Anomaly: ∂µjµ

5 = e2 8π2 Fµν ˜

Fµν

  • 2

3

Integrate out Ψ FCS = µNCS

e2 16π2 Fµν ˜

Fµν = ∂µKµ

  • d

x3K0 = NCS =

α 2π

  • d

x3 A · B

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SLIDE 10

Model Abelian Instabilities

  • A. Florio, Lattice2018, 23/07/18

L = − 1

4FµνFµν + ¯

Ψ/ DΨ +(Dµφ)∗Dµφ − V(φ) with: jµ

5 = ¯

Ψγµγ5Ψ V(φ) = m2|φ|2 + λ|φ|4 Anomaly: ∂µjµ

5 = e2 8π2 Fµν ˜

Fµν

  • 2

3

Integrate out Ψ FCS = µNCS

e2 16π2 Fµν ˜

Fµν = ∂µKµ

  • d

x3K0 = NCS =

α 2π

  • d

x3 A · B k2AA µkAA vs

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SLIDE 11

Model Abelian Instabilities

  • A. Florio, Lattice2018, 23/07/18

L = − 1

4FµνFµν + ¯

Ψ/ DΨ +(Dµφ)∗Dµφ − V(φ) with: jµ

5 = ¯

Ψγµγ5Ψ V(φ) = m2|φ|2 + λ|φ|4 Anomaly: ∂µjµ

5 = e2 8π2 Fµν ˜

Fµν

  • 2

3

Integrate out Ψ FCS = µNCS

e2 16π2 Fµν ˜

Fµν = ∂µKµ

  • d

x3K0 = NCS =

α 2π

  • d

x3 A · B k2AA µkAA vs Instability if k < α

π µ!

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SLIDE 12

Abelian Instabilities Comments

  • A. Florio, Lattice2018, 23/07/18

Integrate out Ψ FCS = µNCS

e2 16π2 Fµν ˜

Fµν = ∂µKµ

  • d

x3K0 = NCS =

α 2π

  • d

x3 A · B k2AA µkAA vs Instability if k < α

π µ!

  • 3

4

  • Long-range gauge fields
  • Symmetric phase
  • Also at non-zero temperature
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SLIDE 13

Comments External Magnetic Field

  • A. Florio, Lattice2018, 23/07/18
  • Long-range gauge fields
  • Symmetric phase
  • Also at non-zero temperature
  • 4

5

EoM + Flux Cons. = ⇒ B vac. state

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SLIDE 14

Comments External Magnetic Field

  • A. Florio, Lattice2018, 23/07/18
  • Long-range gauge fields
  • Symmetric phase
  • Also at non-zero temperature
  • 4

5

EoM + Flux Cons. = ⇒ B vac. state Generating A cost no energy

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SLIDE 15

Comments External Magnetic Field

  • A. Florio, Lattice2018, 23/07/18
  • Long-range gauge fields
  • Symmetric phase
  • Also at non-zero temperature
  • 4

5

EoM + Flux Cons. = ⇒ B vac. state Continuum of vac. NCS ∝ A · B Generating A cost no energy

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SLIDE 16

External Magnetic Field Sum-Up

  • A. Florio, Lattice2018, 23/07/18

EoM + Flux Cons. = ⇒ B vac. state Continuum of vac. NCS ∝ A · B Generating A cost no energy

  • 5

6

  • B = 0: Instability
  • B = 0: Non-trivial vac. structure

Similar to non-abelian!

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SLIDE 17

External Magnetic Field Sum-Up

  • A. Florio, Lattice2018, 23/07/18

EoM + Flux Cons. = ⇒ B vac. state Continuum of vac. NCS ∝ A · B Generating A cost no energy

  • 5

6

  • B = 0: Instability
  • B = 0: Non-trivial vac. structure

Similar to non-abelian!

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SLIDE 18

Overview Lattice Model Results/Outlooks

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SLIDE 19

Lattice Model Real-Time Simulations

  • A. Florio, Lattice2018, 23/07/18

L = − 1

4FµνFµν + (Dµφ)∗Dµφ − V(φ)

−

1 2c2

s (∂0a)2 + 1

2(∂ia)2

with a a scalar field Reproduce EoM U ( 1 ) + A x i

  • n

!

  • 7

8

MC generated thermal ensemble Solve classical EoM tf Measure

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SLIDE 20

Real-Time Simulations Technical Comments

  • A. Florio, Lattice2018, 23/07/18

MC generated thermal ensemble Solve classical EoM tf Measure

  • 8

9

  • Lattice topological F˜

F

  • External mag. field as twisted BCs
  • Homogeneous axion much easier

Refs.: JHEP04(2018)026

j.nuclphysb.2017.12.001

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SLIDE 21

Real-Time Simulations Technical Comments

  • A. Florio, Lattice2018, 23/07/18

MC generated thermal ensemble Solve classical EoM tf Measure

  • 8

9

  • Lattice topological F˜

F

  • External mag. field as twisted BCs
  • Homogeneous axion much easier

Refs.: JHEP04(2018)026

j.nuclphysb.2017.12.001

This work

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SLIDE 22

Overview Lattice Model Results/Outlooks

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SLIDE 23

Chern-Simons Density

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • A ·

B costs E = ⇒ Q2(t) → cst

  • µ = 0, B = 0
  • A ·

B costs E = ⇒ Q2(t) → ΓVt

RD walk

  • 9

10

10−1 101 103 105 10−6 10−5 10−4 t CS Evolution Q2

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SLIDE 24

Chern-Simons Density

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • A ·

B costs E = ⇒ Q2(t) → cst

  • µ = 0, B = 0
  • A ·

B costs E = ⇒ Q2(t) → ΓVt

RD walk

  • 9

11

10−1 101 103 105 10−8 10−6 10−4 10−2 t CS Evolution

e2 = 0.125

Q2

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SLIDE 25

Chern-Simons Density

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • A ·

B costs E = ⇒ Q2(t) → cst

  • µ = 0, B = 0
  • A ·

B costs E = ⇒ Q2(t) → ΓVt

RD walk

  • 9

11

10−1 101 103 105 10−8 10−6 10−4 10−2 t CS Evolution

e2 = 0.125 e2 = 0.5

Q2

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SLIDE 26

Results

  • A. Florio, Lattice2018, 23/07/18

10−1 101 103 105 10−8 10−6 10−4 10−2 t CS Evolution

e2 = 0.125 e2 = 0.5

Q2

  • 11

12

Γ pred. by MHD:

Γth e6B2 ≈ 2.5 · 10−5

Measured Γ:

Γexp e6B2 ≈ 1.5 ± 0.2 · 10−3

Agree on parametric but

Γexp Γth ≈ 60!

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SLIDE 27

Results Next: Chemical Potential

  • A. Florio, Lattice2018, 23/07/18

Γ pred. by MHD:

Γth e6B2 ≈ 2.5 · 10−5

Measured Γ:

Γexp e6B2 ≈ 1.5 ± 0.2 · 10−3

Agree on parametric but

Γexp Γth ≈ 60!

  • 13

14

  • µ = 0, B = 0
  • Lat. art.: µmin = kmin

π α ∝ 1 N

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SLIDE 28

Next: Chemical Potential

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • Lat. art.: µmin = kmin

π α ∝ 1 N

  • 13

14

200 400 10 20 30 t Chemical Potential

N = 16

µ

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SLIDE 29

Next: Chemical Potential

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • Lat. art.: µmin = kmin

π α ∝ 1 N

  • 13

14

10−3 10−1 101 103 105 10 20 30 t Chemical Potential

N = 16

µ

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SLIDE 30

Next: Chemical Potential

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • Lat. art.: µmin = kmin

π α ∝ 1 N

  • 13

14

10−3 10−1 101 103 105 10 20 30 t Chemical Potential

N = 16 N = 224

µ

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SLIDE 31

Next: Chemical Potential

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • Lat. art.: µmin = kmin

π α ∝ 1 N

  • 13

14

10−3 10−1 101 103 105 10 20 30 t Chemical Potential

N = 16 N = 224 N = 420

µ

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SLIDE 32

Next: Chemical Potential

  • A. Florio, Lattice2018, 23/07/18
  • µ = 0, B = 0
  • Lat. art.: µmin = kmin

π α ∝ 1 N

Question: µ independent rate at small µ ?

  • 13

14

10−3 10−1 101 103 105 10 20 30 t Chemical Potential

N = 16 N = 224 N = 420

µ

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SLIDE 33

Further Outlooks

  • A. Florio, Lattice2018, 23/07/18

10−3 10−1 101 103 105 10 20 30 t Chemical Potential

N = 16 N = 224 N = 420

µ

  • 14

15

  • B = 0, µ = 0
  • Hard Thermal Loops
  • Non-homogeneous axion
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SLIDE 34

Further Outlooks

  • A. Florio, Lattice2018, 23/07/18

10−3 10−1 101 103 105 10 20 30 t Chemical Potential

N = 16 N = 224 N = 420

µ

  • 14

15

  • B = 0, µ = 0
  • Hard Thermal Loops
  • Non-homogeneous axion
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SLIDE 35

Further Outlooks

  • A. Florio, Lattice2018, 23/07/18

10−3 10−1 101 103 105 10 20 30 t Chemical Potential

N = 16 N = 224 N = 420

µ

  • 14

15

  • B = 0, µ = 0
  • Hard Thermal Loops
  • Non-homogeneous axion
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SLIDE 36

Further Outlooks Take Away

  • A. Florio, Lattice2018, 23/07/18
  • B = 0, µ = 0
  • Hard Thermal Loops
  • Non-homogeneous axion
  • 15

16

  • Discrepancies between MHD

and full simulations

  • Exciting outlooks
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SLIDE 37

Further Outlooks Take Away

  • A. Florio, Lattice2018, 23/07/18
  • B = 0, µ = 0
  • Hard Thermal Loops
  • Non-homogeneous axion
  • 15

16

  • Discrepancies between MHD and

full simulations

  • Exciting outlooks
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SLIDE 38

Thank you!

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SLIDE 39

Non-Abelian

  • A. Florio, Lattice2018, 23/07/18

1,000 2,000 10 20 30 t Chemical Potential and B µ

  • 1

2

ψ Gµν Instabilities Sphalerons [Rubakov,1986] [Rummukainen,2014]