Asymptotic Safety 2018+

Daniel F Litim

Asymptotic Safety 2018+

Workshop “Asymptotic Safety in a Dark Universe”Perimeter Institute, Waterloo

5 Jun 2018

Daniel F Litim

asymptotic safety in the spotlight

U Manchester1 Jul 2019

Daniel F Litim




asymptotic safetyfrom particle physics to quantum gravity

Daniel F Litim




Daniel F Litim

Daniel F Litim



standard model

local QFT for fundamental interactionsstrong nuclear forceweak forceelectromagnetic force

open challenges

what comes beyond the SM?and how does gravity fit in?

where are we ?

1

2

3

t

b

| |

104 108 1012 1016 1020 1024 1028 1032 1036 1040

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

/GeV

SM Planck LandauStandard Model

Quantum Gravity

Landau pole

Vacuum Metastability

LHC

what is asymptotic safety?

Gross, Wilzcek ’73 , Politzer ‘73

UV fixed point fundamental QFTWilson ’71

asymptotic freedom non-interactingUV fixed point

Weinberg ‘79

asymptotic safety interactingUV fixed point

gauge + matter

quantum gravityChristensen, Duff ’78

Gastmans, Kallosh, Truffin ’78Weinberg ’79

infinite-NF Gross-Neveu Rosenstein, War, Park’ 89de Calan, Faria da Veiga, Magnen, de Seneor ’91

Litim, Sannino ’14Bond, Litim ’16, ’17, ‘18

exact asymptotic safety

Reuter ’96 Litim ’03

infinite-N non-linear sigmainfinite-NF Gross-Neveu Gawedzki, Kupiainen ‘85

Brezin, Zinn-Justin ’76Bardeen, Lee, Shrock ‘76

infinite-N scalars Pisarski ’82Bardeen, Moshe, Bander ‘84

2+eps

3d

4d

4d quantum gravity

why asymptotic safety?Quantum Gravity

UV fixed pointsLHC

1

2

3

t,b

'

-

u

v

104 1010 1016 1022 1028 1034 1040 1046 1052 1058 1064 1070

10-6

10-5

10-4

10-3

10-2

10-1

100

101

/GeV

Model A PlanckBSM

AS models beyond the SM and their phenomenology: Talk by Tom Steudtner (today’s parallel session 1530)

today:understand asymptotic safety in general weakly-coupled 4d QFTs

signatures of asymptotic safetyin quantum gravity

asymptotic safety and models beyond the SM

AD Bond, DF Litim, 1608.00519/EPJC1707.04217/PRDn1709.06953/PRLn1710.07612/PRDn 1801.08527/PRLn

asymptotic safetyin gauge-matter theories

0.00 0.05 0.10 0.15 0.20 0.25-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

�

↵

asymptotic freedom

freeUV fixed point

e.g. QCD

� =d↵

d lnµ

0.00 0.05 0.10 0.15 0.20 0.25-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.00 0.05 0.10 0.15 0.20 0.25-0.10

-0.05

0.00

0.05

0.10

�

↵

infrared freedom

e.g. QED (MSSM, gravity,…)

“Landau pole”

0.00 0.05 0.10 0.15 0.20 0.25-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.00 0.05 0.10 0.15 0.20 0.25-0.10

-0.05

0.00

0.05

0.10

0.00 0.05 0.10 0.15 0.20 0.25-0.10

-0.05

0.00

0.05

0.10

�

↵

asymptotic safety

interacting UV fixed point

“cancellations at quantum level”

path integral

4d QFTs

Z[J ] = exp�i

Zd

4x(L+ Lgf + Lgh + J

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action L =1

4g2aTrF a

µ⌫Fµ⌫a + i ID I +

1

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A)2

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fields vectors , fermions , scalars Aaµ

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I<latexit sha1_base64="JORD6ev32a+Wapu3L4+KYVO/bCo=">AAAB7XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0orcI5gHJEmYns8mY2ZllplcIIf/gxYMiXv0fb/6Nk2QPmljQUFR1090VpVJY9P1vb2V1bX1js7BV3N7Z3dsvHRw2rM4M43WmpTatiFouheJ1FCh5KzWcJpHkzWh4M/WbT9xYodUDjlIeJrSvRCwYRSc1OqkV3btuqexX/BnIMglyUoYctW7pq9PTLEu4Qiapte3ATzEcU4OCST4pdjLLU8qGtM/bjiqacBuOZ9dOyKlTeiTWxpVCMlN/T4xpYu0oiVxnQnFgF72p+J/XzjC+CsdCpRlyxeaL4kwS1GT6OukJwxnKkSOUGeFuJWxADWXoAiq6EILFl5dJ47wS+JXg/qJcvc7jKMAxnMAZBHAJVbiFGtSBwSM8wyu8edp78d69j3nripfPHMEfeJ8/cHOPBg==</latexit><latexit sha1_base64="JORD6ev32a+Wapu3L4+KYVO/bCo=">AAAB7XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0orcI5gHJEmYns8mY2ZllplcIIf/gxYMiXv0fb/6Nk2QPmljQUFR1090VpVJY9P1vb2V1bX1js7BV3N7Z3dsvHRw2rM4M43WmpTatiFouheJ1FCh5KzWcJpHkzWh4M/WbT9xYodUDjlIeJrSvRCwYRSc1OqkV3btuqexX/BnIMglyUoYctW7pq9PTLEu4Qiapte3ATzEcU4OCST4pdjLLU8qGtM/bjiqacBuOZ9dOyKlTeiTWxpVCMlN/T4xpYu0oiVxnQnFgF72p+J/XzjC+CsdCpRlyxeaL4kwS1GT6OukJwxnKkSOUGeFuJWxADWXoAiq6EILFl5dJ47wS+JXg/qJcvc7jKMAxnMAZBHAJVbiFGtSBwSM8wyu8edp78d69j3nripfPHMEfeJ8/cHOPBg==</latexit><latexit sha1_base64="JORD6ev32a+Wapu3L4+KYVO/bCo=">AAAB7XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0orcI5gHJEmYns8mY2ZllplcIIf/gxYMiXv0fb/6Nk2QPmljQUFR1090VpVJY9P1vb2V1bX1js7BV3N7Z3dsvHRw2rM4M43WmpTatiFouheJ1FCh5KzWcJpHkzWh4M/WbT9xYodUDjlIeJrSvRCwYRSc1OqkV3btuqexX/BnIMglyUoYctW7pq9PTLEu4Qiapte3ATzEcU4OCST4pdjLLU8qGtM/bjiqacBuOZ9dOyKlTeiTWxpVCMlN/T4xpYu0oiVxnQnFgF72p+J/XzjC+CsdCpRlyxeaL4kwS1GT6OukJwxnKkSOUGeFuJWxADWXoAiq6EILFl5dJ47wS+JXg/qJcvc7jKMAxnMAZBHAJVbiFGtSBwSM8wyu8edp78d69j3nripfPHMEfeJ8/cHOPBg==</latexit><latexit sha1_base64="JORD6ev32a+Wapu3L4+KYVO/bCo=">AAAB7XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0orcI5gHJEmYns8mY2ZllplcIIf/gxYMiXv0fb/6Nk2QPmljQUFR1090VpVJY9P1vb2V1bX1js7BV3N7Z3dsvHRw2rM4M43WmpTatiFouheJ1FCh5KzWcJpHkzWh4M/WbT9xYodUDjlIeJrSvRCwYRSc1OqkV3btuqexX/BnIMglyUoYctW7pq9PTLEu4Qiapte3ATzEcU4OCST4pdjLLU8qGtM/bjiqacBuOZ9dOyKlTeiTWxpVCMlN/T4xpYu0oiVxnQnFgF72p+J/XzjC+CsdCpRlyxeaL4kwS1GT6OukJwxnKkSOUGeFuJWxADWXoAiq6EILFl5dJ47wS+JXg/qJcvc7jKMAxnMAZBHAJVbiFGtSBwSM8wyu8edp78d69j3nripfPHMEfeJ8/cHOPBg==</latexit>

path integral

4d QFTs

Z[J ] = exp�i

Zd

4x(L+ Lgf + Lgh + J

i�i)

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action L =1

4g2aTrF a

µ⌫Fµ⌫a + i ID I +

1

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1

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fields vectors , fermions , scalars Aaµ

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gauge

Yukawa quartics

“theory space”

gauge

Yukawas

quartics

“theory space”

gauge

Yukawas

free

quartics

“theory space”

gauge

Yukawas

(partially)interacting

quartics

“theory space”

gauge

Yukawas

(fully)interacting

quartics

“theory space”

gauge

Yukawas

R

strict perturbative control: FPs inside sphere for any R 0

quartics

“theory space”

gauge

Yukawas

quartics

N

Y

N

Y

Y

Y

N

Y

Y

N

N

Y

Y

N

Y

“Banks Zaks” “gauge

Yukawa”“scalar

Yukawa”

“scalar”

interacting fixed point

“theory space”

gauge

Yukawas

quartics

weak FPs

N

Y

IR

N

IRUV

Y

Y

Y

N

Y

IR

Y

N

N

no

Y

Y

N

no

Y

N

Y

no

N

Y

Y

Y

N

Y

no

Y

abelian

no

non-abelian

BanksZaks gauge

Yukawascalar

Yukawa

scalargauge

Yukawascalar

Yukawa

scalar

YES NO

BanksZaks

gaugeYukawa

AD Bond, DF Litim, Price of Asymptotic Safety, PRL 122 (2019) 211601 [1801.08527]

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1

G

�<latexit sha1_base64="2IqI+t8FyL1K8k/sZuwvkxwhMDo=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6LHgxWMVWwttKJvtpF262YTdiVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXplIY8rxvp7S2vrG5Vd6u7Ozu7R9UD4/aJsk0xxZPZKI7ITMohcIWCZLYSTWyOJT4GI5vZv7jE2ojEvVAkxSDmA2ViARnZKVWL0Ri/WrNq3tzuKvEL0gNCjT71a/eIOFZjIq4ZMZ0fS+lIGeaBJc4rfQygynjYzbErqWKxWiCfH7s1D2zysCNEm1LkTtXf0/kLDZmEoe2M2Y0MsveTPzP62YUXQe5UGlGqPhiUZRJlxJ39rk7EBo5yYkljGthb3X5iGnGyeZTsSH4yy+vkvZF3ffq/t1lrXFfxFGGEziFc/DhChpwC01oAQcBz/AKb45yXpx352PRWnKKmWP4A+fzB8imjrQ=</latexit><latexit sha1_base64="2IqI+t8FyL1K8k/sZuwvkxwhMDo=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6LHgxWMVWwttKJvtpF262YTdiVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXplIY8rxvp7S2vrG5Vd6u7Ozu7R9UD4/aJsk0xxZPZKI7ITMohcIWCZLYSTWyOJT4GI5vZv7jE2ojEvVAkxSDmA2ViARnZKVWL0Ri/WrNq3tzuKvEL0gNCjT71a/eIOFZjIq4ZMZ0fS+lIGeaBJc4rfQygynjYzbErqWKxWiCfH7s1D2zysCNEm1LkTtXf0/kLDZmEoe2M2Y0MsveTPzP62YUXQe5UGlGqPhiUZRJlxJ39rk7EBo5yYkljGthb3X5iGnGyeZTsSH4yy+vkvZF3ffq/t1lrXFfxFGGEziFc/DhChpwC01oAQcBz/AKb45yXpx352PRWnKKmWP4A+fzB8imjrQ=</latexit><latexit sha1_base64="2IqI+t8FyL1K8k/sZuwvkxwhMDo=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6LHgxWMVWwttKJvtpF262YTdiVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXplIY8rxvp7S2vrG5Vd6u7Ozu7R9UD4/aJsk0xxZPZKI7ITMohcIWCZLYSTWyOJT4GI5vZv7jE2ojEvVAkxSDmA2ViARnZKVWL0Ri/WrNq3tzuKvEL0gNCjT71a/eIOFZjIq4ZMZ0fS+lIGeaBJc4rfQygynjYzbErqWKxWiCfH7s1D2zysCNEm1LkTtXf0/kLDZmEoe2M2Y0MsveTPzP62YUXQe5UGlGqPhiUZRJlxJ39rk7EBo5yYkljGthb3X5iGnGyeZTsSH4yy+vkvZF3ffq/t1lrXFfxFGGEziFc/DhChpwC01oAQcBz/AKb45yXpx352PRWnKKmWP4A+fzB8imjrQ=</latexit><latexit sha1_base64="2IqI+t8FyL1K8k/sZuwvkxwhMDo=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6LHgxWMVWwttKJvtpF262YTdiVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXplIY8rxvp7S2vrG5Vd6u7Ozu7R9UD4/aJsk0xxZPZKI7ITMohcIWCZLYSTWyOJT4GI5vZv7jE2ojEvVAkxSDmA2ViARnZKVWL0Ri/WrNq3tzuKvEL0gNCjT71a/eIOFZjIq4ZMZ0fS+lIGeaBJc4rfQygynjYzbErqWKxWiCfH7s1D2zysCNEm1LkTtXf0/kLDZmEoe2M2Y0MsveTPzP62YUXQe5UGlGqPhiUZRJlxJ39rk7EBo5yYkljGthb3X5iGnGyeZTsSH4yy+vkvZF3ffq/t1lrXFfxFGGEziFc/DhChpwC01oAQcBz/AKb45yXpx352PRWnKKmWP4A+fzB8imjrQ=</latexit>

confined

UV free

renormalisation group


1

2

BZG


confined

UV free

confi

ned



1

2 3

BZG


confined

UV free

GY

confi

ned

confi

ned



1

2 3

4

UV GYBZG


confined

confined

IR free

UV free

GY

confi

ned

confi

ned



1

2 3

4

5

UV GYBZG


confined

IR fr

ee

confined

IR free

UV free

GY

confi

ned

confi

ned

confi

ned


�

Y4

GY

G BZ

�

Y4

G BZ

�

Y4

G

�

Y4

GY

G

a) b)

c) d)

Yukawa

gauge

BZ

BZ

GY

GY

GG

G G

α

Y4

G

Yuk

awa

gaugeUV

strong

asymptotic freedom

α

Y4

GY

GY

ukaw

a

gaugeIR

strong

weak

UV fixed point

asymptotic safety

1 4

“enhanced predictivity"

“theory space”

gauge

Yukawas

quartics

weak FPs

N

Y

IR

N

IRUV

Y

Y

Y

N

Y

IR

Y

N

N

no

Y

Y

N

no

Y

N

Y

no

N

Y

Y

Y

N

Y

no

Y

abelian

no

non-abelian

BanksZaks gauge

Yukawascalar

Yukawa

scalargauge

Yukawascalar

Yukawa

scalar

YES NO

BanksZaks

gaugeYukawa

proofs of fixed points & asymptotic safety

simple gauge theories with matter

semi-simple SU(N) x SU(M) gauge theories with matter

supersymmetric gauge theories with matter

DF Litim, F Sannino, Asymptotic Safety Guaranteed, 1406.2337 (JHEP)

AD Bond, DF Litim, More Asymptotic Safety Guaranteed, 1707.04217 (PRD)

AD Bond, DF Litim, Asymptotic Safety Guaranteed in Supersymmetry, 1709.06953 (PRL)

AD Bond, DF Litim, G Medina Vazquez, T Steudtner, Conformal window for asymptotic safety, 1710.07615 (PRD)

higher order interactions in gauge theories with matterT Buyukbese, DF Litim, Asymptotic Safety Beyond Marginal Interactions, PoS LATTICE2016 (2017) 233

general theorems for fixed pointsAD Bond, DF Litim, Theorems for Asymptotic Safety of Gauge Theories, 1608.00519 (EPJC)AD Bond, DF Litim, Price of Asymptotic Safety, 1801.08527 (PRL)

A Bond, G Hiller, K Kowalska, DF Litim, Directions for model building from asymptotic safety, JHEP1708 (2017) 004

phenomenology and models beyond the Standard ModelG Hiller, C Hermigos-Feliu, DF Litim, T Steudtner, Asymptotically safe extensions of the Standard Model and their flavour phenomenology, Moriond (EW2019) 1905.11020

simple

DF Litim, F Sannino, Asymptotic Safety Guaranteed, 1406.2337 (JHEP)

SU(N)+1 Yukawa+2 quartics

(NF fermions+ mesons)

α

Y4

GY

G

Yuk

awa

gaugeIR

strong

weak

UV fixed point

asymptotic safety

semi-simple

SU(N) x SU(M)+ 2 Yukawas+ 5 quartics

various fermionsand mesons

1

2

4

5

8

9

UV

IR

AS

AD Bond, DF Litim, More Asymptotic Safety Guaranteed, 1707.04217 (PRD)

what about supersymmetry?


�

Y4

GY

G BZ

�

Y4

G BZ

�

Y4

G

�

Y4

GY

G

a) b)

c) d)

Yukawa

gauge

BZ

BZ

GY

GY

GG

G G N=0 SUSY

�

Y4

GY

G BZ

�

Y4

G BZ

�

Y4

G

�

Y4

GY

G

a) b)

c) d)

Yukawa

gauge

BZ

BZ

GY

GY

GG

G G N=1 SUSY

not available

�

Y4

GY

G BZ

�

Y4

G BZ

�

Y4

G

�

Y4

GY

G

a) b)

c) d)

Yukawa

gauge

BZ

BZ

GY

GY

GG

G G N=2 SUSY

not available

not available

not available

�

Y4

GY

G BZ

�

Y4

G BZ

�

Y4

G

�

Y4

GY

G

a) b)

c) d)

Yukawa

gauge

BZ

BZ

GY

GY

GG

G G N=4 SUSY

not available

not available

not available

not available

G

IR

UV

↵1

↵2

Susy UV fixed point

SU(N)xSU(M)+ super- potential


“Susyenhances

predictivity"

gauge coupling

competition between matter and gauge fields

� = �B ↵2 + C ↵3 +O(↵4)↵ =g2

(4⇡)2

weakly coupled fixed point 0 < ↵⇤ = B/C ⌧ 1

why no UV BZ?

C =2

11

h2SF

2

�11CF

2 + 7CG2

�+ 2SS

2

�11CS

2 � CG2

�� 17BCG

2

i

CS2 <

1

11CG

2must have

> 0 > 0

why no UV BZ?

asymptotic safety

E8

E7E6F4

G2

SOHNLSpHNLSUHNL

5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

38

12

111

23

712

1318

1924

1

N

c

� =min C2(R)

C2(adj)

Bond, Litim, 1608.00519/EPJC

weakly coupledBZ are never UV asymptotic safety

here’s why.

impossible!

summary

AD Bond, DF Litim, Price of Asymptotic Safety, PRL 122 (2019) 211601 [1801.08527]

asymptotic safety requires all types of matter fields Yukawa couplings are keyworks with supersymmetry

implications

particle physics: UV complete 4D theories (free or safe) require non-abelian gauge fields

universality class of any weakly coupled 4D critical point contains non-abelian gauge fields

“any QFT under pert. control in the deep UV or IR asymptotes to a conformal field theory”

any weakly-coupled 4D conformal field theory contains gauge degrees of freedom

Polchinski ’88Luty, Polchinski, Rattazzi, ‘12

asymptotic freedom and asymptotic safety are two sides of one and the same medal

implications


universality class of any weakly coupled 4D critical point contains non-abelian gauge fields


any weakly-coupled 4D conformal field theory contains gauge degrees of freedom

Polchinski ’88Luty, Polchinski, Rattazzi, ‘12

new BSM territory to UV-completethe Standard Model

implications


statistical physics: universality class of any weakly coupled 4D critical point contains non-abelian gauge fields


any weakly-coupled

Polchinski ’88Luty, Polchinski, Rattazzi, ‘12systematic classification of

weak critical points in 4D

implications



conformal field theory: any weakly-coupled 4D CFT contains non-abelian gauge fields

“any QFT under perturbative control in the deep UV or IR asymptotes to a conformal field theory” Polchinski ’88

Luty, Polchinski, Rattazzi, ‘12

implications




QFT offers infinitely many 4D CFTsaccess to CFT datacomplementary to conformal bootstrap

implications




asymptotic safety BSM

A Bond, G Hiller, K Kowalska, DF Litim, Directions for model building from asymptotic safety, JHEP1708 (2017) 004G Hiller, C Hermigos-Feliu, DF Litim, T Steudtner, Asymptotically safe extensions of the Standard Model and their flavour phenomenology, Moriond (EW2019) 1905.11020

asymptotic safetybeyond the SM

i(R3, R2, Y )

Sij

flavors of BSM fermionsBSM singlet scalars

NF

SU(3)C ⇥ SU(2)L ⇥ U(1)YSM gauge symmetry

features: vector-like fermionsU(NF )⇥ U(NF )global flavor symmetry

minimal framework:

single BSM Yukawa coupling

AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727 (JHEP)

U(1)Y BSMBSM matter charged under U(1)Y

lower bounds on hypercharge

a3

a2a y

matching

scale

cross - over scale

R3 = 1, R2 = 4, NF = 12

1000 104 105 10610-4

0.001

0.01

0.1

1

m HGeVL

a3

a y

a2

matching

scale

cross - over scale

R3 = 10, R2 = 1, NF = 30

1000 2000 5000 1 ¥ 104 2 ¥ 10410-4

0.001

0.01

0.1

1

m HGeVL

R3 = 10, R2 = 4, NF = 80

a ya3

a2

matching

scalecross - over scale

1000 2000 5000 1 ¥ 104 2 ¥ 10410-5

10-4

0.001

0.01

0.1

1

m HGeVL

R3 = 10, R2 = 4, NF = 80

a2

a y

a3

matching

scale

cross - over scale

2 ¥ 1010 5 ¥ 1010 1 ¥ 1011 2 ¥ 1011 5 ¥ 1011 1 ¥ 101210-4

0.001

0.01

0.1

1

m HGeVL

cros

s-ov

er I

FP4

(model C)cr

oss-

over

II

mat

chin

g sc

ale

FP2

R3 = 10, R2 = 4, NF = 80

a y

a3

a2

matching scale cross - over scale

5 ¥ 1010 1 ¥ 1011 2 ¥ 1011 5 ¥ 1011 1 ¥ 1012

0.001

0.002

0.005

0.010

0.020

0.050

0.100

0.200

m HGeVL

R3 = 3, R2 = 4, NF = 290

a y

a3

matching scale

cross- over scale

a2

1000 10 00050002000 30001500 7000

0.001

0.002

0.005

0.010

0.020

0.050

0.100

m HGeVL

low scale low scale low scale

low scalehigh scale

high scale

A FP2i)

C FP4iv) C FP2v)

B FP3ii) C FP3iii)

D FP4vi)

UV fixed points

LHC exclusion boundslower limits on the mass of long-lived colored particles that form QCD bound states; exclusion data from ATLAS & CMS (pair production)

AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727 (JHEP)

1 2 5 10 20 50 100 2001

2

5

10

20

50

100

My @TeVD

MS@Te

VD

LHCmax. interference

ference

R hadronsearches

BSM

di-jet limits

(10,1,30)

interno

Model B(10,1,30)

mass exclusion limits

*) fudged from 13 TeVATLAS + CMS gluino analysis

*)

1702.01727

fixed pointsin quantum gravity

gravitationphysics of classical gravity

Einstein’s theory of general relativity

GN = 6.7⇥ 10�11 m3

kg s3

⇤ ⇡ 10�35s�2

Rµ⌫ � 1

2gµ⌫R = �⇤ gµ⌫ + 8⇡GN Tµ⌫

Newton’s coupling

cosmological constant

what’s new with gravity?

Newton’s coupling is dimensionful

degrees of freedom: spin 2

[GN ] = 2�D < 0perturbatively non-renormalisable

asymptotic safety requires largeanomalous dimensions

non-perturbative tools mandatory

coupling

fermions

gluons

D = 2 + ✏ : ↵ = GN (µ)µD�2

D = 2 + ✏ : ↵ = gGN(µ)µ2�D

D = 4 + ✏ : ↵ = g2YM(µ)µ4�D

Gastmans et al ’78Christensen, Duff ’78

Weinberg ’79Kawai et al ’90

Gawedzki, Kupiainen ’85de Calan et al ’91

Peskin ’80Morris ’04

scalars Brezin, Zinn-Justin ’76Bardeen, Lee, Shrock ’76D = 2 + ✏ : ↵ = gNL(µ)µ

D�2

classes ofgauge-Yukawa theories

D = 4 : several ↵i Litim, Sannino ’14

dimension

gravitons

µ/⇤T

G(µ) ⇡ GN

G(µ) ⇡ ↵⇤µD�2

classical GR0.01 0.1 1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

UV

IR

↵/↵⇤

Einstein-Hilbert

UV fixed pointimplies

weakened gravity

quantum GR

beyond EH

effective action with invariants up to mass dimension D = 2(N � 1)

Ricci scalars �k / f(R)

S =

Zd

4x

pdetgµ⌫

1

16⇡G

[�R+ 2⇤] +N�1X

n=2

�n Rn�k



S =

Zd

4x

pdetgµ⌫

1

16⇡G

[�R+ 2⇤] +N�1X

n=2

�n Rn

bootstrap search strategy Falls, DL, Nikolakopoulos, Rahmede ’13, ’14

1 fix N, compute RG flow2 deduce fixed point and exponents3 increase N to N+1 and start over at 1

�k

beyond EH



Falls, Litim, Schroeder ’18

up to order N = 2 N = 3 N = 7N = 11 N = 35 N = 71

Codello, Percacci, Rahmede ’07

Falls, Litim, Nikolakopoulos, Rahmede ’13, ’14, ’16

Bonanno, Contillo,, Percacci ’10

Souma, ‘99, Reuter, Lauscher ’01, Litim ’03

Reuter, Lauscher ’01

S =

Zd

4x

pdetgµ⌫

1

16⇡G

[�R+ 2⇤] +N�1X

n=2

�n Rn�k

beyond EH

f(R)

5 10 15 20 25 30 350

10

20

30

40

N

�n(N)

h�ni+ cn

5 10 15 20 25 30 35

-20

0

20

40

60

N

#n(N)

UV scaling exponents

Falls, Litim, Nikolakopoulos, Rahmede 1301.41911410.4815

good

conv

erge

nce

4

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10

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30

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N=

near-Gaussian strip

R

“as Gaussian as it gets”

Falls, DL, Nikolakopoulos, Rahmede ’13, ’14, ’16Falls, DL, Schroeder, ’18

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10

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-6-4-20246

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relevant

0 5 10 15 20

0

10

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nFalls, King, DL, Nikolakopoulos, Rahmede, ’18

�k =

Zd

dx

pg[Fk(Ric

2) +R · Zk(Ric2)]

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relevantirrelevant

#n(N)near-Gaussian strip

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0 4 8 12 16-10

0

10

20

30

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n

FP4 N

N

2

4

6

8

10

12

14

16

18

N

Riemann

Yannick Kluth, DL, Bad Honnef Workshop March 2019 (in prep.)

�k =

Zd

dx

pg[Fk(Riem

2) +R · Zk(Riem2)]

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signature of weak coupling

near-Gaussian scaling

10

20

30

40

50

60

70N

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0 10 20 30 40 50 60 70

1

0.1

0.01

0.001

5 13 21 29 37 45 53 61 69 N

n

|vn(N)|

v exp(�n/ne)

weak “effective” coupling

Falls, DL, Nikolakopoulos, Rahmede ’13, ’14, ‘16Falls, DL, Schroeder, ’18

vn = 1� #n(N)

#n,G<latexit sha1_base64="Tk+jpp7aHB+c3RJ5IfBJhgOPb8w=">AAACH3icbVBdS8MwFE3n15xfVR99CQ5hgo5WRH0RBgr6JBPcB6ylpFm6haVpSdLBKP0nvvhXfPFBEfFt/8Z028OcHgicnHPvTe7xY0alsqyxUVhaXlldK66XNja3tnfM3b2mjBKBSQNHLBJtH0nCKCcNRRUj7VgQFPqMtPzBTe63hkRIGvEnNYqJG6IepwHFSGnJMy9SR4RwmHn82j51AoFw6gyRUH2ikMcrD8fZ3D3lJ3n1XZZ5ZtmqWhPAv8SekTKYoe6Z3043wklIuMIMSdmxrVi5qZ5MMSNZyUkkiREeoB7paMpRSKSbTvbL4JFWujCIhD5cwYk635GiUMpR6OvKEKm+XPRy8T+vk6jgyk0pjxNFOJ4+FCQMqgjmYcEuFQQrNtIEYUH1XyHuIx2S0pGWdAj24sp/SfOsaltV+/G8XLudxVEEB+AQVIANLkEN3IM6aAAMnsEreAcfxovxZnwaX9PSgjHr2Qe/YIx/AKMXo1c=</latexit><latexit sha1_base64="Tk+jpp7aHB+c3RJ5IfBJhgOPb8w=">AAACH3icbVBdS8MwFE3n15xfVR99CQ5hgo5WRH0RBgr6JBPcB6ylpFm6haVpSdLBKP0nvvhXfPFBEfFt/8Z028OcHgicnHPvTe7xY0alsqyxUVhaXlldK66XNja3tnfM3b2mjBKBSQNHLBJtH0nCKCcNRRUj7VgQFPqMtPzBTe63hkRIGvEnNYqJG6IepwHFSGnJMy9SR4RwmHn82j51AoFw6gyRUH2ikMcrD8fZ3D3lJ3n1XZZ5ZtmqWhPAv8SekTKYoe6Z3043wklIuMIMSdmxrVi5qZ5MMSNZyUkkiREeoB7paMpRSKSbTvbL4JFWujCIhD5cwYk635GiUMpR6OvKEKm+XPRy8T+vk6jgyk0pjxNFOJ4+FCQMqgjmYcEuFQQrNtIEYUH1XyHuIx2S0pGWdAj24sp/SfOsaltV+/G8XLudxVEEB+AQVIANLkEN3IM6aAAMnsEreAcfxovxZnwaX9PSgjHr2Qe/YIx/AKMXo1c=</latexit><latexit sha1_base64="Tk+jpp7aHB+c3RJ5IfBJhgOPb8w=">AAACH3icbVBdS8MwFE3n15xfVR99CQ5hgo5WRH0RBgr6JBPcB6ylpFm6haVpSdLBKP0nvvhXfPFBEfFt/8Z028OcHgicnHPvTe7xY0alsqyxUVhaXlldK66XNja3tnfM3b2mjBKBSQNHLBJtH0nCKCcNRRUj7VgQFPqMtPzBTe63hkRIGvEnNYqJG6IepwHFSGnJMy9SR4RwmHn82j51AoFw6gyRUH2ikMcrD8fZ3D3lJ3n1XZZ5ZtmqWhPAv8SekTKYoe6Z3043wklIuMIMSdmxrVi5qZ5MMSNZyUkkiREeoB7paMpRSKSbTvbL4JFWujCIhD5cwYk635GiUMpR6OvKEKm+XPRy8T+vk6jgyk0pjxNFOJ4+FCQMqgjmYcEuFQQrNtIEYUH1XyHuIx2S0pGWdAj24sp/SfOsaltV+/G8XLudxVEEB+AQVIANLkEN3IM6aAAMnsEreAcfxovxZnwaX9PSgjHr2Qe/YIx/AKMXo1c=</latexit><latexit sha1_base64="Tk+jpp7aHB+c3RJ5IfBJhgOPb8w=">AAACH3icbVBdS8MwFE3n15xfVR99CQ5hgo5WRH0RBgr6JBPcB6ylpFm6haVpSdLBKP0nvvhXfPFBEfFt/8Z028OcHgicnHPvTe7xY0alsqyxUVhaXlldK66XNja3tnfM3b2mjBKBSQNHLBJtH0nCKCcNRRUj7VgQFPqMtPzBTe63hkRIGvEnNYqJG6IepwHFSGnJMy9SR4RwmHn82j51AoFw6gyRUH2ikMcrD8fZ3D3lJ3n1XZZ5ZtmqWhPAv8SekTKYoe6Z3043wklIuMIMSdmxrVi5qZ5MMSNZyUkkiREeoB7paMpRSKSbTvbL4JFWujCIhD5cwYk635GiUMpR6OvKEKm+XPRy8T+vk6jgyk0pjxNFOJ4+FCQMqgjmYcEuFQQrNtIEYUH1XyHuIx2S0pGWdAj24sp/SfOsaltV+/G8XLudxVEEB+AQVIANLkEN3IM6aAAMnsEreAcfxovxZnwaX9PSgjHr2Qe/YIx/AKMXo1c=</latexit>

“effective” couplings

Daniel F Litim



5 Jun 2018

conclusions

Daniel F Litim



5 Jun 2018

complete understanding of asymptotic safety at weak coupling

Daniel F Litim



5 Jun 2018

complete understanding of asymptotic safety at weak coupling works for

simple, semi-simple and supersymmetric

gauge theories, large variety of

fixed points

Daniel F Litim



5 Jun 2018




fixed points window of opportunities for model building,BSM physics, dark matter, …

Daniel F Litim



5 Jun 2018




fixed points window of opportunities for model building,BSM physics, dark matter, … progress for

asymptotic safety at strong coupling

w or w/o gravity




fixed points window of opportunities for model building,BSM physics, dark matter, … progress for

asymptotic safety at strong coupling

w or w/o gravity

Documents

Asymptotic Safety 2018+