konstantin zarembo (nordita, stockholm)...gravity “ordinary”, but strong interactions and title...
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Do we live in extra dimensions?
Konstantin Zarembo(Nordita, Stockholm)
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We don’t know …
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Kaluza-Klein theory
Gravity in (4+1)d = Gravity in (3+1)d + ElectromagentismKaluza’21Klein’26
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Kaluza-Klein theory (ctd)
(3+1)d
Uncertainty relation:
Can be very big if R is small
Current exp. bounds:
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Extra dimensions can arise dynamically,
if interactions among constituents in a system are
very strong
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Standard Model of elementary particles
Theoretical basis:
Quantum field
Force
Particle
Wave
Ø Quantum Field Theory
Ø Gauge Symmetry
Ø General Relativity
Space-time geometryGravitational force
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Standard Model (ctd)
• describes basic constituents of matter and interactions among them
• accuracy reaches 0.1% on average, at weak coupling
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Standard Model (ctd)
• Incomplete:ü experiment: dark matter, neutrino oscillations, …
ü theory: hierarchy problem, UV completion, …
ü esthetic: too many ad hoc parameters, accidental symmetries, …
• Not well understood at strong coupling:ü no theory of “strong” strong interactions
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Example: Anomalous Magnetic Moment
gyromagnetic ratio
Quantum Mechanics:
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Anomalous Magnetic Moment (ctd)
Vacuum polarization:
Angular momentum: shared between electron and photon
Magnetic moment: carried by electron only
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Anomalous Magnetic Moment (ctd)
Schwinger’48
Current state of the art:
most accurately known quantity in physics!
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Anomalous Magnetic Moment: Muon
Ø The 3.4σ difference: is it due to physics beyond the Standard Model?
Ø Theoretical error cannot be made smaller
q Prades, de Rafael, Vainshtein’09
Irreducible uncertaintly due to strong quark interactions
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Coulomb field vs. Flux tube(QED) (QCD)
string carries constantenergy per unit length
q q
confinement
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From Bali, Phys. Rep. 343 (2001) 1
More refined lattice simulations clearly indicate that string fluctuates.Caselle,Fiore,Gliozzi,Hasenbusch,Provero’97; Caselle,Pepe,Rago’04; …
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From Bornyakov,Ichie,Mori,Pleiter,Polikarpov,Scierholz,Streuer,Stüben,Suzuki’04
Energy density distribution inside baryon
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String theory vs. Lattice simulations
From Dubovsky, Flauger and Gorbenko, JETP 120 (2015) 399
worldsheet axion (new d.o.f. !)
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What is String theory?
Particle String
In space-time:
time
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StringsParticles
String Interactions
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Common lore:
• open strings = mesons
• closed strings = glueballs
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Regge trajectoriesString tension
From Ebert, Faustov and Galkin, Phys. Rev. D79 (2009) 114029
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Consider as a small parameter
Large-N expansion‘t Hooft’74
- the number of colors
Two coupling constants:‘t Hooft coupling:
string coupling: small
“large”
(N=3)
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Planar diagrams and strings
time
Large-N limit:
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Strings and quantum gravity
ØDifferent vibrational modes of the string = different particles
ØThe first mode (ground state) describes spin-2, m=0 particle – this is graviton!
Ø Selfconsistency of string propagation in curvedspace-time = Einstein’s equations
String theory = A theory of quantum gravity
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Holography
5D bulk
4D boundary
z
0
Maldacena’97
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Anti-de-Sitter space (AdS5)
5D bulk
4D boundary
z
0
Scale (conformal) invariance:
AdS/CFT correspondence
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AdS/CFT correspondence Maldacena’97
Gubser,Klebanov,Polyakov’98Witten’98
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Super-Yang-Mills
Strings simple
complicatedsimple
complicated
Strong/weak coupling duality
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Extra dimension as energy scale
z
0
Small 4d distances/large energies
Large 4d distances/small energies
Small z
Large z
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z
0
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Dynamically generated scale
“IR wall”
UV boundary
Black Hole horizonor
domain wall
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Holography and strongly-coupled plasma
5D black hole
Black Hole inside AdS
Gauge-theory plasma
Temperature of the plasma = Hawking temperature of BH
Witten’98
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Black holes and hydrodynamics
BH horizon
Einstein equations (bulk)
Navier-Stokes equations (boundary)
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Oscillation modes of black-hole space-time(quasi-normal modes)
Sound waves in the plasma
Viscosity of quark-gluon plasma is of the same order of magnitude.
viscosity
entropy density
Policastro,Son,Starinets’01Kovtun,Son,Starinets’04
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AdS/CMT
CFT
AdS
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Spin chains
Color ordering:
Evolution operator:
spin-chain Hamiltonian
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Constituent gluons 1d spins
(1+1)d quantum systems are often exactly solvable!
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• Consistency (and) symmetry conditions on the S-matrix
• Map to 2d statistical systems
• Map to 2d Conformal Field Theory
Yang-Baxter equationYang’67Baxter’72Zamolodchikov’78Faddeev,Sklyanin,Takhtajan’78
Baxter’72
Bazhanov,Lukyanov,Zamolodchikov’94-98Fioravanti,Rossi’01,03
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Exact non-perturbative solution for the AdS/CFT spectrum
was found by methods of integrable systemsGromov,Kazakov,Vieira’09Arutyunov,Frolov’09Bombardelli,Fioravanti,Tateo’09
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Spin chain String
Magnons String vibrations
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ConclusionsØ Extra dimensions can emerge
“holographically”, due to strong interactions Ø (Quantum) gravity is an integral part of the
holographic dualityØ Many questions in holography can be
addressed using integrable systems
Holography is a language that translates
between
Quantumgravity
“Ordinary”, but strong interactions
and