Viability of quantum-gravity induced ultraviolet completions for - - PowerPoint PPT Presentation

▶
viability of quantum gravity induced ultraviolet
SMART_READER_LITE
LIVE PREVIEW

Viability of quantum-gravity induced ultraviolet completions for - - PowerPoint PPT Presentation

Feb 17, 2024 473 likes •1.1k views

Viability of quantum-gravity induced ultraviolet completions for matter Aaron Held based on work with Astrid Eichhorn 1705.02342 Institut fr Theoretische Physik, Universitt Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

slide-1
SLIDE 1

Viability of quantum-gravity induced ultraviolet completions for matter

based on work with Astrid Eichhorn 1705.02342

Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

Aaron Held

slide-2
SLIDE 2

Standard Model

Buttazzo et.Al. ‘13, 1307.3536

1

slide-3
SLIDE 3

Standard Model Standard Model Landau poles

18 free parameters

Buttazzo et.Al. ‘13, 1307.3536

1

slide-4
SLIDE 4

Standard Model Standard Model

18 free parameters

P l a n c k s c a l e p h y s i c s

Buttazzo et.Al. ‘13, 1307.3536

1

slide-5
SLIDE 5

Question:

Can quantum gravity provide a UV completion for the Standard Model?

2

slide-6
SLIDE 6

What I have to tell ...

(1) concepts of asymptotic safety (& the FRG) (2) global symmetries and the fixed-point structure (3) good approximations: spin-2 rules (4) observational constraints on gravity couplings

(a) weak-gravity bound (b) linking electroweak- (IR) and Planck-scale physics

3

slide-7
SLIDE 7

Asymptotic safety & the FRG

4

slide-8
SLIDE 8

5

Asymptotic freedom

g UV gUV = 0 Scale invariance at a Gaussian fixed point (GFP) ensures a free (perturbatively renormalizable) UV theory

slide-9
SLIDE 9

Asymptotic safety

g UV gUV = const Scale invariance at a non-Gaussian fixed point (NGFP) ensures a safe (non- perturbatively renormalizable) UV theory

5

Asymptotic freedom

g UV gUV = 0 Scale invariance at a Gaussian fixed point (GFP) ensures a free (perturbatively renormalizable) UV theory

slide-10
SLIDE 10

Asymptotic safety conjecture

  • UV-attractive (relevant) direction:

needs to be fixed by experiment

  • UV-repulsive (irrelevant) direction: prediction of asymptotic safety

6

  • existence of a UV fixed

point for metric field theory (fundamental theory)

Weinberg ‘80

  • finite number of UV-

attractive directions (predictivity)

slide-11
SLIDE 11

Asymptotic safety conjecture

Flows towards IR

Weinberg ‘76

7

slide-12
SLIDE 12

Asymptotic safety conjecture

Flows towards IR

UV-attractive (relevant)

Weinberg ‘76

7

slide-13
SLIDE 13

UV-repulsive (irrelevant)

Asymptotic safety conjecture

Flows towards IR 7

Weinberg ‘76

UV-attractive (relevant)

slide-14
SLIDE 14
  • UV-attractive (relevant):

consistent with any IR value

Asymptotic safety conjecture

8

Weinberg ‘76

slide-15
SLIDE 15
  • UV-attractive (relevant):

consistent with any IR value

Asymptotic safety conjecture

  • UV-repulsive (irrelevant):

predictive

8

Weinberg ‘76

slide-16
SLIDE 16

functional RG

quantum effective action RG-scale dependent effective action

9

microscopic action prediction of asymptotic safety

slide-17
SLIDE 17

functional RG

flow equation

RG-scale dependent effective action

Wetterich ‘93

9

quantum effective action RG-scale dependent effective action microscopic action prediction of asymptotic safety

slide-18
SLIDE 18

functional RG

Full regularized propagator super trace (incl. loop momentum) RG-scale dependent effective action

Wetterich ‘93

9

quantum effective action microscopic action prediction of asymptotic safety

slide-19
SLIDE 19

functional RG

Full regularized propagator regulator insertions super trace (incl. loop momentum) RG-scale dependent effective action

Wetterich ‘93

9

Gies ‘06, 0611146

quantum effective action microscopic action prediction of asymptotic safety

slide-20
SLIDE 20

functional RG

Full regularized propagator super trace (incl. loop momentum) RG-scale dependent effective action

manifestly 1-loop

Wetterich ‘93

9

microscopic action prediction of asymptotic safety

regulator insertions

Gies ‘06, 0611146

quantum effective action

slide-21
SLIDE 21

fermion scalar fluctuating metric

9

functional RG

Full regularized propagator super trace (incl. loop momentum) RG-scale dependent effective action

manifestly 1-loop

Wetterich ‘93

microscopic action prediction of asymptotic safety

regulator insertions

Gies ‘06, 0611146

quantum effective action

slide-22
SLIDE 22

RG-flows:

truncation and regulator dependence

Theory space

Gies ‘06, 0611146

  • Regulators chosen to

maintain UV/IR limits

  • Truncations also alter

fixed point action ➔ choice of truncation is crucial

10

slide-23
SLIDE 23

11

Global symmetries at the UV FP

Maximally-symmetric asymptotic safety

slide-24
SLIDE 24

Global symmetries at the UV FP

12

slide-25
SLIDE 25

Global symmetries at the UV FP

12

slide-26
SLIDE 26

Global symmetries at the UV FP

13

slide-27
SLIDE 27

Global symmetries at the UV FP

13

slide-28
SLIDE 28

scalar Z2 symmetry chiral U(1) symmetry U(1) phase symmetry scalar shift symmetry combined discrete chiral symmetry

Global symmetries at the UV FP

finally interested in

14

slide-29
SLIDE 29

15

How to set up truncations

spin-2 rules

slide-30
SLIDE 30

Spin-2 rules

16

slide-31
SLIDE 31

The traceless-transverse mode dominates (confirmed in all results)

Newton coupling cosmological constant higher curvature

Scalar curvature couplings are sub-leading

Spin-2 rules

16

slide-32
SLIDE 32

Suppression of matter-mediated effects

. . .

direct gravity contributions matter-mediated

17

slide-33
SLIDE 33

Suppression of matter-mediated effects

direct gravity contributions matter-mediated spin-2 mode only including trace mode including 4-fermion-mediated full result

17

slide-34
SLIDE 34

(4) Observational constraints

(a) Weak-Gravity Bound

18

slide-35
SLIDE 35

~ gn+m

gravitational induction

➢ gravity induces all matter interactions sharing the global symmetries

  • f the matter kinetic terms

19

Weak-Gravity Bound

slide-36
SLIDE 36

➢ gravity induces all matter interactions sharing the global symmetries

  • f the matter kinetic terms

➢ at lowest order

quartic couplings

➢ Lowest momentum

  • rder

➢ same for gauge fields Christiansen & Eichhorn, 2017

~ g2 ~ gn+m

gravitational induction

Weak-Gravity Bound

19

slide-37
SLIDE 37

canonical dimension pure matter

vanishing fixed-point value at possible

20

Weak-Gravity Bound

slide-38
SLIDE 38

canonical dimension pure matter mixed induced

Weak-Gravity Bound

20

slide-39
SLIDE 39

canonical dimension pure matter mixed induced

g = 0 g = 3 g = 6

Eichhorn, Held, Pawlowski ‘16, 1604.02041

Weak-Gravity Bound

20

slide-40
SLIDE 40
  • Weak gravity bound:
  • Too strong gravity

leads to an unstable matter sector

  • these bounds occur

for all matter types

canonical dimension pure matter mixed induced

g = 0 g = 3 g = 6

Eichhorn, Held, Pawlowski ‘16, 1604.02041

Weak-Gravity Bound

20

slide-41
SLIDE 41

The traceless-transverse mode dominates (confirmed in all results)

Newton coupling cosmological constant higher curvature

Weak-Gravity Bound

21

slide-42
SLIDE 42

The traceless-transverse mode dominates (confirmed in all results)

Newton coupling cosmological constant higher curvature

Weak-Gravity Bound

Eichhorn & Held ‘17, 1705.02342

21

slide-43
SLIDE 43

The traceless-transverse mode dominates (confirmed in all results)

Newton coupling cosmological constant higher curvature

Weak-Gravity Bound

similar bound arises in a U(1) gauge theory

Christiansen & Eichhorn, 2017, 1702.07724

21

slide-44
SLIDE 44

The traceless-transverse mode dominates (confirmed in all results)

Newton coupling cosmological constant higher curvature

21

Weak-Gravity Bound

Eichhorn & Held ‘17, 1705.02342

slide-45
SLIDE 45

(4) Observational constraints

(b) Linking electroweak- (IR) and Planck-scale physics

22

slide-46
SLIDE 46

Linking electroweak- (IR) and Planck-scale physics

Buttazzo et.Al. ‘13, 1307.3536

23

slide-47
SLIDE 47

Christiansen & Eichhorn ‘17, 1702.07724 Folkerts, Litim, Pawlowski ‘11, 1101.5552 Harst & Reuter ‘10, 1101.6007 Shaposhnikov & Wetterich ‘10, 0912.0208

this talk all SM couplings

  • are marginal
  • do not share global kinetic

symmetries

  • Gravity acts as anomalous

dimension

Buttazzo et.Al. ‘13, 1307.3536

23

Linking electroweak- (IR) and Planck-scale physics

slide-48
SLIDE 48

all SM couplings

  • are marginal
  • do not share global kinetic

symmetries

  • Gravity acts as anomalous

dimension

23

Linking electroweak- (IR) and Planck-scale physics

slide-49
SLIDE 49

all SM couplings

  • are marginal
  • do not share global kinetic

symmetries

  • Gravity acts as anomalous

dimension

. . .

#TT > 0 #TT < 0 SM

Eichhorn & Held ‘17, 1705.02342

23

Linking electroweak- (IR) and Planck-scale physics

slide-50
SLIDE 50

#TT > 0 #TT < 0 SM 23

all SM couplings

  • are marginal
  • do not share global kinetic

symmetries

  • Gravity acts as anomalous

dimension

. . .

#TT < 0 relevant

Linking electroweak- (IR) and Planck-scale physics

Eichhorn & Held ‘17, 1705.02342

slide-51
SLIDE 51

all SM couplings

  • are marginal
  • do not share global kinetic

symmetries

  • Gravity acts as anomalous

dimension

. . .

#TT > 0

#TT > 0 #TT < 0 SM 23

irrelevant

Phenomenological viability bound forbids #TT > 0

Linking electroweak- (IR) and Planck-scale physics

Eichhorn & Held ‘17, 1705.02342

slide-52
SLIDE 52

Phenomenological viability bound

recall

Newton coupling cosmological constant higher curvature

24

in tension with massive fermions In agreement with massive fermions

Eichhorn & Held ‘17, 1705.02342

slide-53
SLIDE 53

Preliminary: predictive power

25

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

slide-54
SLIDE 54

Preliminary: predictive power

25

recall

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

Eichhorn & Held ‘17, 1705.02342

slide-55
SLIDE 55

Preliminary: predictive power

recall g = 0

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

25

Eichhorn & Held ‘17, 1705.02342

slide-56
SLIDE 56

g = 0.01

Preliminary: predictive power

recall

25

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

Eichhorn & Held ‘17, 1705.02342

slide-57
SLIDE 57

Preliminary: predictive power

g = 0.05

25

recall

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

Eichhorn & Held ‘17, 1705.02342

slide-58
SLIDE 58

Preliminary: predictive power

g = 0.1

25

recall

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

Eichhorn & Held ‘17, 1705.02342

slide-59
SLIDE 59

Preliminary: predictive power

g = 0.5

25

recall

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

Eichhorn & Held ‘17, 1705.02342

slide-60
SLIDE 60

Preliminary: predictive power

g = 1

25

recall

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

Eichhorn & Held ‘17, 1705.02342

slide-61
SLIDE 61

Preliminary: predictive power

g = 1

Combined asymptotic safety with:

  • one Gaußian attractive

direction

  • one non-Gaußian irrelevant /

predictive direction

➢ flavour hierarchy

25

recall

  • complex SU(2)-scalar
  • left-handed SU(2)-doublet
  • and two right-handed singlets

charge conjugated

Eichhorn & Held ‘17, 1705.02342

slide-62
SLIDE 62

Conclusions

  • maximally symmetric

asymptotic safety

  • recovering the SM allows to

constrain the quantum gravity regime

  • weak gravity bound
  • phenomenological viability

bound

  • natural mechanism for flavour

hierarchy

26

Eichhorn & Held ‘17, 1705.02342