EmergentLorentzInvariance from&Strong&Dynamics&

Oriol Pujolàs

IFAE & Universitat Autònoma de Barcelona

Emergent Lorentz Invariance from Strong Dynamics

Gauge/Gravity Duality 2013 MPI Munich

30/7/13

Based on

arXiv:1305.0011 w/ G. Bednik, S. Sibiryakov

+ work in progress w/ M. Baggioli

Motivation

Can Lorentz Invariance be an accidental symmetry ?

Context: Hořava Gravity

recovery of LI at low energies is the most pressing issue phenomenologically

δcψ ψγ iDiψ δcγ2 B2 δcH

2 |DiH |2 (CPT even)

Motivation

Observational bounds: |cp − cγ |<10−20 !!| ce − cγ | < 10

−15 !


2 |DiH |2

EFT expectation: δc 1−10−3!!!

FINE TUNING

Collins Perez Sudarsky Urrutia Vucetich ‘04

Iengo Russo Serone ‘09

Giudice Strumia Raidal ‘10

Anber Donoghue ‘11

(CPT even)

Motivation

Observational bounds: |cp − cγ |<10−20 !!| ce − cγ | < 10

−15 !


2 |DiH |2

EFT expectation: δc 1−10−3!!!

FINE TUNING

Collins Perez Sudarsky Urrutia Vucetich ‘04

Iengo Russo Serone ‘09

Giudice Strumia Raidal ‘10

Anber Donoghue ‘11

(CPT even)

Challenge: can we achieve naturally ~ 10

-20 suppression?

Motivation

RG & Lorentz Invariance

LI-fixed point is IR-attractive !! Chadha Nielsen’ 83


LI-fixed point is IR-attractive !! Chadha Nielsen’ 83

δc = δc0

[1−β g02 log(µ /M)]βδcβ

g 2 = g02

1− β g02 log(µ /M)

δcψ k 2

δcH k 2

g

@ 1 loop:

E.g., LV – Yukawa theory: L = (∂h)2 +ψ γ ⋅∂ψ +ghψψ + δc's

(4π )2 d δcd logµ

= βδ c g2 δc

(4π )2 d gd logµ

= β g3


LI-fixed point is IR-attractive !!

E.g., LV – Standar Model (SME)

Giudice Strumia Raidal’ 10


LI


In weakly coupled theories, LI emergens, but very slowly!

Suppression is only for a factor Log ΛUV

ΛIR

⎛⎝⎜

⎞⎠⎟ 10

LI

LI

let’s accelerate the running by turning to strong coupling


Idea:

δc=µβ*g*

2

(4π )2δc0Near a strongly-coupled fixed point:

accelerated running


= βδ c g2 δc


Idea:

δc=µβ*g*

2

(4π )2δc0Near a strongly-coupled fixed point:

accelerated running


= βδ c g2 δc


power > 0 granted ( )

LV deformation

Unitarity bound

=> is an irrelevant coupling

Dim ∂µφ ∂νφ( ) ≥ 4

βδc > 0

δc

δc ∂tφ∂tφ

Lifshitz / LV boundary condition

AdS

IR UV

Dual to a CFT + UV cutoff (coupling to LV gravity, )

+ IR cutoff (confining, )

LV-Randall-Sundrum

ΛQCD

Bednik OP Sibiryakov ‘13

MP

L = LCFT (OΔ ) −φ w2 − c2k2( )φ +λφOΔ

LV-Randall-Sundrum

RS Realizes a CFT with an operator and a LV source OΔ φ

∂5Φ = (w 2 − c2k2 )Φ

probe scalar with LV boundary

5−M2( )Φ = 0

L = LCFT (OΔ ) −φ w2 − c2k2( )φ +λφOΔ

LV-Randall-Sundrum

RS Realizes a CFT with an operator and a LV source OΔ φ

Gφ (w, k)−1 w2 − c2k2 + λ2 (p2 )Δ−2

if relevant (Δ< 3)

=> Emergent LI

λ

wi2 (k2 ) mi

2 + (1+ δci2)k2 + k2+2n

M (i, n)2n∑

LV-Randall-Sundrum

δci

2 δcUV

2

λ2ΛIR

ΛUV

⎛⎝⎜

⎞⎠⎟

2(3−Δ )

power-law suppressed! for relevant couplings (Δ < 3 )

Schematic form of the dispersion relations: Bednik OP Sibiryakov ‘13

(Optimal case, Δ=2)

wi2 (k2 ) mi

2 + (1+ δci2)k2 + k2+2n

M (i, n)2n∑

LV-Randall-Sundrum

δci

2 δcUV

2

λ2ΛIR

ΛUV

⎛⎝⎜

⎞⎠⎟

2(3−Δ )

power-law suppressed! for relevant couplings (Δ < 3 )

Schematic form of the dispersion relations: Bednik OP Sibiryakov ‘13

(Optimal case, Δ=2)

Lifshitz Holography

ds2 =

2

r2dr2 + r

2

2d x 2− r 2 z

2zdt 2

Kachru Liu Mulligan ‘08

z > 1

Lifshitz solutions in Einstein + Proca + Λ :

z=1

z = d-1

m2L2

At ∝ r z

ds2 = g(r)

2

r2dr2 + r

2

2d x 2− f (r)r

2 z

2zdt 2

Kachru Liu Mulligan ‘08

Lifshitz

At

AdS

log(r)

Lifshitz Holography

δGφ (w, k)

−1 (p2 )Δ−2 1+ w2 (p2 )(Δ1 −5)

Λ*2(Δ1−4)

+(p2 )(Δ−2)

Λ*2(Δ−1) + ...

⎛⎝⎜

⎞⎠⎟+ ...

⎡

⎣⎢

⎤

⎦⎥

The flow imprints modified scaling into the scalar propagator

δc2

(ΛIR LUV )2(Δ1 −4)

(ΛIR LUV )2(3−Δ )⎧⎨⎪

⎩⎪

... and into the dispersion relations of bound states


Lifshitz Holography

δGφ (w, k)

−1 (p2 )Δ−2 1+ w2 (p2 )(Δ1 −5)

Λ*2(Δ1−4)

+(p2 )(Δ−2)

Λ*2(Δ−1) + ...

⎛⎝⎜

⎞⎠⎟+ ...

⎡

⎣⎢

⎤

⎦⎥


δc2

(ΛIR LUV )2(Δ1 −4)

(ΛIR LUV )2(3−Δ )⎧⎨⎪

⎩⎪


In the simplest model – not very large suppression Δ1 ≤ 4.35


Lifshitz Holography

δGφ (w, k)

−1 (p2 )Δ−2 1+ w2 (p2 )(Δ1 −5)

Λ*2(Δ1−4)

+(p2 )(Δ−2)

Λ*2(Δ−1) + ...

⎛⎝⎜

⎞⎠⎟+ ...

⎡

⎣⎢

⎤

⎦⎥


δc2

(ΛIR LUV )2(Δ1 −4)

(ΛIR LUV )2(3−Δ )⎧⎨⎪

⎩⎪


In the simplest model – not very large suppression Δ1 ≤ 4.35


Lifshitz Holography

can be made arbitrarily large w/ non-minimal couplings Baggioli OP w.i.p.

Conclusions

RG + Strong Dynamics => fast Emergence of LI is possible

Emergent LI may not be an exceptional phenomenon

The leading LV corrections are characterized by an exponent

determined by the LILVO – least irrelevant LV operator

-‐> RG scale = compositeness scale

-‐> how large can be ?? δc Λ IR

ΛUV

⎛⎝⎜

⎞⎠⎟ΔLILVO − 4

ΔLILVO

Application to Condensed Matter

Discussion

– Is ELI already at work in some material?

– QED3 has been argued to exhibit ELI

– Related phenomenon: emergence of isotropy

Implications in Particle Physics / Non-Relativistic Gravity

Discussion

compositeness – at low Energies ~ 100 TeV

Limits on compositeness in SM? Λ ≥ few10TeV

compositeness – at low Energies ~ 100 TeV

Limits on compositeness in SM? Λ ≥ few10TeV

Implications in Particle Physics / Non-Relativistic Gravity

Discussion

Several QFT-‐mechanisms for Emergence of LI NR SUSY (Groot-‐Nibelink Pospelov ’04) , Large N species (Anber Donoghue ’11)

Via naturalness, NRQG becomes very predictive: new physics at much lower energies

105 GeV 1015 GeV

Thank you!

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EmergentLorentzInvariance from&Strong&Dynamics&