Oriol Pujolàs
description
Transcript of Oriol Pujolàs
Oriol PujolàsIFAE & Universitat Autònoma de Barcelona
Emergent Lorentz Invariance from
Strong Dynamics
Holography: From Gravity to Quantum
Matter
Isaac Newton Institute for Mathematical
Sciences
16/9/13
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
In this talk,
1) LV:
2) Gravity (mostly) turned offbounds from gravity: MLV≤10
15GeV
dynamical preferred frame ”AETHER” uμ
Poincaré → SO(3)⊗ translations
uμ =MLV (1, 0, 0, 0)timelike vev
Motivation
δcψ ψγ iDiψ δcγ
2rB2 δcH
2 |DiH |2 (CPT even)
Motivation
Observational bounds:|cp −cγ|<10−20 !!
| ce −cγ|<10−15 !
δcψ ψγ iDiψ δcγ
2rB2 δcH
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 !
δcψ ψγ iDiψ δcγ
2rB2 δcH
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
RG & Lorentz Invariance
LI-fixed point is IR-attractive !! Chadha Nielsen’ 83
δc =δc0
[1−β g02log(μ /M)]
β δc
β
g 2 =g02
1− β g02 log(μ /M)
δcψ k
r 2
δcH kr 2
g
@ 1 loop:
E.g., LV – Yukawa theory:
(4π )2d g
dlogμ=β g3
RG & Lorentz Invariance
LI-fixed point is IR-attractive !!
E.g., LV – Standar Model (SME)
Giudice Strumia Raidal’ 10
RG & Lorentz Invariance
LI
RG & Lorentz Invariance
In weakly coupled theories, LI emerges... very slowly!
Suppression is only by a factor
Log ΛUV
ΛIR
⎛
⎝⎜⎞
⎠⎟: 10
LI
LI
let’s accelerate the running by turning to strong coupling
RG & Lorentz Invariance
Idea:
δc=μβ*g*
2
(4π )2δc0Near a strongly-coupled fixed point:
accelerated running
RG & Lorentz Invariance
Idea:
δc=μβ*g*
2
(4π )2δc0Near a strongly-coupled fixed point:
accelerated running
RG & Lorentz Invariance
power > 0 granted ( )
LV deformation
Unitarity bound
=> is an irrelevant coupling
Dim ∂μφ ∂νφ( ) ≥4
βδc > 0
δc
δc ∂tφ∂tφsuggests that ELI should not be an exceptional phenomenon
Toy model #1: LV Randall-Sundrum
Lifshitz / LV boundary condition
AdS
IR UV
Dual to a CFT + UV cutoff (coupling to LV gravity, )
+ IR cutoff (confining, )
LV-Randall-Sundrum
ΛQCD
MP
L =LCFT (OΔ ) −φ w2 −c2k2( )φ +λφOΔ
LV-Randall-Sundrum
RS Realizes a CFT with an operator and a LV sourceOΔ φ
∂5Φ = (w 2 − c2k2 )Φ
probe scalar with LV boundary
W5−M2( )Φ =0
Bednik OP Sibiryakov ‘13
L =LCFT (OΔ ) −φ w2 −c2k2( )φ +λφOΔ
LV-Randall-Sundrum
RS Realizes a CFT with an operator and a LV sourceOΔ φ
if relevant (Δ< 3)
=> Emergent LI
λ
Bednik OP Sibiryakov ‘13
wi2 (k2 ) ; mi
2 + (1+δci2)k2 +
k2+2n
M(i, n)2n∑
LV-Randall-Sundrum
δci
2 :δcUV
2
λ 2ΛIR
ΛUV
⎛
⎝⎜⎞
⎠⎟
2(3−Δ)
power-law suppressed!for relevant couplings (Δ < 3 )
Dispersion relations of bound-states: 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
λ 2ΛIR
ΛUV
⎛
⎝⎜⎞
⎠⎟
2(3−Δ)
power-law suppressed!for relevant couplings (Δ < 3 )
Bednik OP Sibiryakov ‘13
(Optimal case, Δ=2)
Dispersion relations of bound-states:
Toy model #2: Lifshitz flows
Lifshitz Holography
ds2 =
l 2
r2 dr2 +r2
l 2 drx2−
r 2 z
l 2zdt2
Kachru Liu Mulligan ‘08
z >1
Lifshitz solutions in Einstein + Proca + Λ :
z=1
z = d-1
m2L2
At ∝ r z
ds2 =g(r)
l 2
r2 dr2 +r2
l 2 drx2− f(r)
r 2 z
l 2zdt2
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
Qualitative agreement with Gubser ‘time warp’ geometries
Bednik OP Sibiryakov ’13
Lifshitz Holography
Gubser ‘08
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 ;
(ΛIRLUV )2(Δ1 −4)
(ΛIRLUV )2(3−Δ)
⎧⎨⎪
⎩⎪
... and into the dispersion relations of bound states
Bednik OP Sibiryakov ’13
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 ;
(ΛIRLUV )2(Δ1 −4)
(ΛIRLUV )2(3−Δ)
⎧⎨⎪
⎩⎪
... and into the dispersion relations of bound states
In the simplest model – not very large suppression Δ1 ≤ 4.35
Bednik OP Sibiryakov ’13
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 ;
(ΛIRLUV )2(Δ1 −4)
(ΛIRLUV )2(3−Δ)
⎧⎨⎪
⎩⎪
... and into the dispersion relations of bound states
In the simplest model – not very large suppression Δ1 ≤ 4.35
Bednik OP Sibiryakov ’13
Lifshitz Holography
can be made arbitrarily large w/ non-minimal couplings Baggioli & OP in progress
Conclusions
RG + Strong Dynamics => fast Emergence of LI
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 : ΛIR
ΛUV
⎛
⎝⎜⎞
⎠⎟
ΔLILVO − 4
ΔLILVO
Application to Condensed Matter
Discussion
– Is there (universal) ELI 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 TeVLimits on compositeness in SM? Λ ≥few10TeV
compositeness – at low Energies ~ 100 TeVLimits on compositeness in SM? Λ ≥few10TeV
Implications in Particle Physics / Non-Relativistic Gravity
Discussion
Several QFT-mechanisms for Emergence of LINR 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!