Fundamental theories of nature -...

Francesco Sannino

Fundamental theories of natureRealising the Wilson’s dream

Plan• Meaning of fundamental

• Asymp. safe theories in 4D

• Large Nf asymptotic safety

• Asymptotically safe standard model

• SUSY-like radiative symmetry breaking

• Exact nonperturbative results for N=1 supersymmetric safety

• New paths in (astro)particle physics

• Theoretical challenges and opportunities

Abel, Bajc, Cacciapalgia, De Andrea, Intriligator, Rishke, Strumia

Alanne, Antipin, Dondi, Gertov, Gillioz, Hansen, Langaeble, Meroni, Mojaza, Mølgaard, Pelaggi, Salvio, Tesi, Thomsen, Vigiani, Z.W. Wang,….

Gauge: SU(3) x SU(2) x U(1) at EW scale

Standard Model

Interactions:

Gauge fields + fermions + scalars

Yukawa: Fermion masses/Flavour

Scalar self-interaction

Fields:

Culprit: Higgs

Gauge - Yukawa theoriesL = �1

2F

2 + iQ�µDµQ+ y(QLHQR + h.c.)

Tr⇥DH

†DH

⇤� �uTr

⇥(H

†H)

2⇤� �vTr

⇥(H

†H)

⇤2

4D: standard model, dark matter, …

Lower D: condensed matter, phase transitions, graphene

4D plus: extra dimensions, string theory, …

Gauge

Yukawa

Scalar selfinteractions

Universal description of physical phenomena

Wilson: A fundamental theory has an UV fixed point

Trivial fixed point Interacting fixed point

-1.0 -0.5 0.00.0

0.1

0.2

0.3

0.4

Log(μ/μ0)

α(μ)

Asymptotic freedom

-1.0 -0.5 0.0 0.50.0

0.1

0.2

0.3

0.4

Log(μ/μ0)

α(μ)

Asymptotic safety

Non-interacting in the UV

Logarithmic scale depend.

Integrating in the UV

Power law

Fundamental theory

Is the Standard Model safe?

Pelaggi, Sannino, Strumia, Vigiani 1701.01453

Do theory like these exist?

Precise and/or nonperturbative exact results for UV interacting fixed points

Exact 4D Interacting UV Fixed Point

Litim and Sannino, 1406.2337, JHEP

Tr⇥@H†@H

⇤� uTr

⇥(H

†H)

2⇤� vTr

⇥(H

†H)

⇤2

L = �F2 + iQ� ·DQ+ y(QLHQR + h.c.)+

Antipin, Gillioz, Mølgaard, Sannino 1303.1525 PRD

Litim, Mojaza, Sannino, 1501.03061, JHEP

Veneziano LimitNormalised couplings

At large NNF

NC2 <+

v

u=

↵v

↵hNF


Litim, Mojaza, Sannino, 1501.03061, JHEP

ϵ

αg

β g

✏ =NF

NC� 11

2

Impossible in Gauge Theories with Fermions alone Caswell, PRL 1974

Complete asymptotic safety

Scalars are needed perturbatively to make the theory fundamental

Gauge + fermion + scalars theories can be fund. at any energy scale


⇤

Gauged Higgs UV Fixed Point Pelaggi, Sannino, Strumia, Vigiani, 1701.01453

Controllably safe in all couplings

Higgs as shoelace

Safe, naturally• A theory without a UV cutoff is technically natural with(out) scalars

• No quadratic divergences can emerge because of IR/UV conformality

• Higgs mass is independent on the intrinsic UV from IR

• All masses only sensitive to new physical thresholds

• IR Conformal symmetry works as chiral symmetry for fermion masses

• New states needed to make the SM safe must be around the TeV corner

Pelaggi, Sannino, Strumia, Vigiani, 1701.01453

Conformal Window 2.0: Large Nf Story

Sannino, ERG 2016, Heidelberg

Antipin and Sannino, 1709.02354

Safe QCDNf

Nc

Must exist a critical Safe Nf

Unsafe region in Nf-Nc

Continuous (Walking) transition?NAF

f

N IRf

NSafef


Antipin and Sannino, 1709.02354 Pica and Sannino 1011.5917, PRD

Safe QCD: Conformal Window 2.0


2 3 4 5 6 70

10

20

30

40

50

60

70

Nc

Nf

IR conformal QC

D

Safe QCD

�⇤m

Nf!1! (N2c � 1)

2NcNf

Antipin and Sannino, 1709.02354Palanques-Mestre, Pascual, Commun. Math. Phys. 84Gracey, PLB, 96, Holdom PLB 2011Pica and Sannino 1011.5917, PRD

Safe Adj QCD: Conformal Window 2.0

Sannino, ERG 2016, Heidelberg Antipin and Sannino, 1709.02354

2 3 4 5 6 70

2

4

6

8

10

Nc

Nf

IR conformal Adjoint QCD

Safe Adjoint QCD

Large Nf (Standard Model)

��(�) ⟷�(�)��(�) ⟷ ��(�)��(�) ⟷ ��(�)�

��

-�

�

�

�

�

�

��

� = Δ� α / �π

� �(�)

@↵i

@ lnµ= �↵i = �SM

↵i+ �extra

↵i

�extra↵i

=↵2i

2⇡�bi +

↵2i

3⇡Fi(�bi

↵i

4⇡)

�bY =4

3Y 2NFDR2DR3 �b2 =

2

3NFDR3

�b3 =2

3NFDR2

F1(A) ⌘ 2

Z A

0I1(x)dx

Fn(A) ⌘Z A

0I1(x)In(x) for n = 2, 3

A ⌘ �b↵

4⇡

Abel, Sannino 1707.06638Pelaggi, Plascencia, Salvio, Sannino, Smirnov, Strumia 1708.00437Mann, Meffe, Wang, Sannino, Steele, Zhang 1707.02942

Antipin and Sannino, 1709.02354Palanques-Mestre, Pascual, Commun. Math. Phys. 84Gracey, PLB, 96, Holdom PLB 2011Pica and Sannino 1011.5917, PRD

Paths to a Safe Standard Model

Large Nf resummation via vector-like fermions [Mann et al. 1707.02942, Pelaggi et al. 1708.00437]

(Perturbative) safety via dynamical breaking, [Abel, Sannino 1707.06638, Bond et al.1702.01727 ]

New paths not yet explored

Large Nf Safe Standard Model QCD can be either free [1708.00437] or safe [1707.02942]

Remaining couplings can be treated perturbatively [1707.06638]

�(1)�H

|SM = (4⇡)2d�H

d ln µ̄= 24�2

H+ �H

�12y2

t� 9g22�3g2

Y

�+

9g428

+3g4

Y

8+

3g22g2Y

4� 6y4

t

Example(s) from 1707.02942

��

��

��

��

��

��

��

��

��

��

λ�

�

�

��

�b2 = �bY =2

3NF , �b3 = 0

Add vector-like leptons & RH neutrinos

Large theory space at our disposal

Higgs fine tuning can be tamed

Supersymmetric (un)safetyIntriligator and Sannino, 1508.07413, JHEP

Exact results beyond perturbation theory

Bajc and Sannino, 1610.09681, JHEP

Bajc Dondi Sannino, 1709.07436

Unitarity constraintsOperators belong to unitary representations of the superconf. group

Dimensions have different lower bounds

Gauge invariant spin zero operators

Chiral primary operators have dim. D and U(1)R charge R

Central chargesPositivity of coefficients related to the stress-energy trace anomaly

‘a(R)’ Conformal anomaly of SCFT = U(1)R ’t Hooft anomalies [proportional to the square of the dual of the Rieman Curvature]

‘c(R)’ [proportional to the square of the Weyl tensor]

‘b(R)’ [proportional to the square of the flavor symmetry field strength]

a-theoremFor any super CFT besides positivity we have, following Cardy

ri = dim. of matter rep.

+(-) for asymptotic safety (freedom)

Stronger constraint for asymp. safety, since at least one large R > 5/3

SQCD with H

W = yTrQHeQ

Nf > 3Nc

AF is lost

No perturbative UV fixed point

SQCD with HAssume a nonperturbative fixed point, however

D(H) =3

2R(H) = 3

Nc

Nf< 1 for Nf > 3Nc

Violates the unitarity bound

D(O) � 1

Potential loophole: H is free and decouples at the fixed point

Check if SQCD without H has an UV fixed point

SQCDUnitarity bound is not sufficient

Non-abelian SQED with(out) H cannot be asymptotically safe

Can be ruled out via a-theorem

aUV�safe � aIR�safe < 0

Generalisation to several susy theories using a-maximisation*

Safe SUSY mechanics

At leat one large R-charge for some of the fields

UV-Interacting to IR-Interacting can be achieved with moderate R-

charges [First non-SUSY example Esbensen-Ryttov-Sannino 1512.04402 ]

Adding IR/UV relevant operators to modify the flow

To avoid the Intriligator-Sannino constraints


Bajc,Dondi, Sannino, 1709.07436Bond Litim, 1709.06953

SUSY GUTs

Exact results


Asymptotic safety

-1.0 -0.5 0.00.0

0.1

0.2

0.3

0.4

Log(μ/μ0)

α(μ)

-1.0 -0.5 0.0 0.50.0

0.1

0.2

0.3

0.4

Log(μ/μ0)

α(μ)

ChSB/Confinement

1 GeV ~ TeV Before Planck

↵s

µ

Light quarks

Top partners

Colorons

Gluino-like

Unexpected

Safe QCDSannino, 1511.09022

Pica & Sannino,1011.5917 PRD

New coloured states

Higgs mechanism

Top

CosmologyCosmic raysLHC

Asymptotic safety

-1.0 -0.5 0.00.0

0.1

0.2

0.3

0.4

Log(μ/μ0)

α(μ)

-1.0 -0.5 0.0 0.50.0

0.1

0.2

0.3

0.4

Log(μ/μ0)

α(μ)

ChSB/Confinement

1 GeV~ TeV

Before Planck

↵s

µ

Testing safe QCD scenariosSannino, 1511.09022

Asymptotic freedom is not a must for UV complete theories

Bond, Hiller, Kowalska, Litim 1702.01727Pelaggi, Sannino, Strumia, Vigiani 1701.01453

Model independent tests of new coloured states at the LHC Becciolini, Gillioz, Nardecchia, Sannino, Spannowsky 1403.7411, PRD

Explore different paths for a safe extension of the SM

Extend the number of (super) safe theories

Cosmological and (astro) particle physics consequences

Different implementations of radiative symmetry breaking

Gravity gauge-gravity duality

Gauge-gauge duality

Safe QCD on the lattice

Interplay with gravity

Worlds of possibilities

We pursue fundamental theories of Nature

Safe Dark Matter

Safe DM

� / ↵q↵X

m4V

µ2

X X

SM SM

V

h�annvi /↵q↵X

m4V

m2X

X

XSM

SM

V

Offset direct detection

Sannino & Shoemaker, 1412.8034, PRD

Fundamental theories of nature -...

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