Holograms of Strings - Department of Physics - University of Virginia

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Decompose the stress tensor <strong>of</strong> a CFT into an equilibrium piece and a non-equilibrium part, with the latter expanded in gradients, which are taken to be small: T µν = T eq µν + Π µν , T eq µν = (ɛ + P)U µ U ν + Pg µν ( ) Π µν = −ησ µν + ητ 〈 Π U · ∇σ µν〉 + 1 3 ∇ · Uσµν ) +κ (R 〈µν〉 − 2U ρ U σ R ρ〈µν〉σ +λ 1 σ 〈µ ρσ ν〉ρ + λ 2 σ 〈µ ρΩ ν〉ρ + λ 3 Ω 〈µ ρΩ ν〉ρ + . . . where σ and Ω are the fluid’s shear and vorticity tensors: σ µν = 2∇ 〈µ U ν〉 ≡ 1 2 ∆µρ ∆ νσ (2∇ ρ U σ + 2∇ σ U ρ ) − 1 3 ∆µν ∆ ρσ 2∇ ρ u σ Ω µν = 1 2 ∆µρ ∆ νσ (∇ ρ U σ − ∇ σ U ρ ) and where ∆ µν are transverse (to the fluid’s velocity) projectors.
◮ Compute the fluid’s response to a small, slowly varying gravitational perturbation, and derive Kubo-type formulae for 2nd order hydro coefficients. [Moore, Sohrabi 2010] ∫ 〈T µν (z)〉 h = 〈T µν 〉 h=0 − 1 2 d 4 µν ρσ x G ra (z; x)h ρσ (x) ∫ ∫ d 4 x d 4 µν ρσ τζ y G raa (z; x, y)h ρσ (x)h τζ (y) + . . . + 1 8 ◮ Solve the conservation law ∇ µ T µν = 0, iteratively, in the fluid’s velocity U µ , and order-by-order in the metric fluctuations =⇒ get Kubo-type formulae! [Arnold, DV, Wu, Xiao, 2011]
Page 1 and 2: Holograms of Strings Diana Vaman Ph
Page 3 and 4: Introduction to String Theory t x P
Page 5 and 6: Introduction to String Theory Strin
Page 7 and 8: Introduction to String Theory But,
Page 9 and 10: For a space-time filling D-brane S
Page 11 and 12: Superstrings Supersymmetry relates
Page 13 and 14: How to think of AdS 5 × S 5 ? S 5
Page 15 and 16: Holography Maldacena: The 4d maxima
Page 17 and 18: µ x h h µυ ρσ z=0 bulk gravito
Page 19 and 20: ◮ mesons? these are q¯q bound st
Page 21 and 22: In the lab, QGP is created in relat
Page 23 and 24: If the deconfined quarks and gluons
Page 25 and 26: Veltman’s circling rules can be t
Page 27 and 28: Jet quenching Jet: a colimated spra
Page 29 and 30: The question: how far does a locali
Page 31 and 32: The source q 0 q 0 q 3 q 0 q 3 L
Page 33: Hydrodynamics- long wavelength/long
Page 37 and 38: lim k 1 →0 k 2 →0 lim k 1 →0
Page 39 and 40: Start with the symmetries. Schrodin
Page 41: Thanks! I would like to thank my pa

Holograms of Strings - Department of Physics - University of Virginia

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