Cold planar horizons are floppy

Cold planar horizons are floppy Cold planar horizons are floppy Jorge E Santos New frontiers in dynamical gravity In collaboration with Sean A Hartnoll - arXiv:1402.0872 and arXiv:1403.4612 / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs Near horizon geometries of extremal planar black holes capture the dissipative dynamics of novel phases of T = quantum matter / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs Near horizon geometries of extremal planar black holes capture the dissipative dynamics of novel phases of T = quantum matter Extensive classification exists for translational invariant systems / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs Near horizon geometries of extremal planar black holes capture the dissipative dynamics of novel phases of T = quantum matter Extensive classification exists for translational invariant systems A more realistic model needs to account for a ubiquitous property of CMT systems: breaking translational invariance / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs Near horizon geometries of extremal planar black holes capture the dissipative dynamics of novel phases of T = quantum matter Extensive classification exists for translational invariant systems A more realistic model needs to account for a ubiquitous property of CMT systems: breaking translational invariance What this talk is not: / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs Near horizon geometries of extremal planar black holes capture the dissipative dynamics of novel phases of T = quantum matter Extensive classification exists for translational invariant systems A more realistic model needs to account for a ubiquitous property of CMT systems: breaking translational invariance What this talk is not: ∂x is broken explicitly in all matter sectors / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs Near horizon geometries of extremal planar black holes capture the dissipative dynamics of novel phases of T = quantum matter Extensive classification exists for translational invariant systems A more realistic model needs to account for a ubiquitous property of CMT systems: breaking translational invariance What this talk is not: ∂x is broken explicitly in all matter sectors For other setups recall Jerome’s talk / 15 Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory Near horizon geometries of AdS black holes describe the low energy dissipative dynamics of strongly interacting QFTs Near horizon geometries of extremal planar black holes capture the dissipative dynamics of novel phases of T = quantum matter Extensive classification exists for translational invariant systems A more realistic model needs to account for a ubiquitous property of CMT systems: breaking translational invariance What this talk is not: ∂x is broken explicitly in all matter sectors For other setups recall Jerome’s talk What I am going to describe doesn’t happen in such setups / 15 Cold planar horizons are floppy What about AdS4 ? Disorder in AdS4 : One periodic source does not do, what about many? 13 / 15 Cold planar horizons are floppy What about AdS4 ? Disorder in AdS4 : One periodic source does not do, what about many? Nx −1 Nw −1 Φs (x, w, 0) = 2V¯ Ai Bj cos[k(i) x + γi ] cos[q(j) w + λj ] , i=1 j=1 13 / 15 Cold planar horizons are floppy What about AdS4 ? Disorder in AdS4 : One periodic source does not do, what about many? Nx −1 Nw −1 Φs (x, w, 0) = 2V¯ Ai Bj cos[k(i) x + γi ] cos[q(j) w + λj ] , i=1 j=1 where γi and λj are random phases, and Φs is the source for operator of ∆+ = 13 / 15 Cold planar horizons are floppy What about AdS4 ? Disorder in AdS4 : One periodic source does not do, what about many? Nx −1 Nw −1 Φs (x, w, 0) = 2V¯ Ai Bj cos[k(i) x + γi ] cos[q(j) w + λj ] , i=1 j=1 where γi and λj are random phases, and Φs is the source for operator of ∆+ = Averaged quantities are defined as: Nx −1 f R ≡ lim 2π lim Nw →+∞ Nx →+∞ i=1 dγi 2π Nw −1 j=1 2π dδj f 2π 13 / 15 Cold planar horizons are floppy What about AdS4 ? Disorder in AdS4 : One periodic source does not do, what about many? Nx −1 Nw −1 Φs (x, w, 0) = 2V¯ Ai Bj cos[k(i) x + γi ] cos[q(j) w + λj ] , i=1 j=1 where γi and λj are random phases, and Φs is the source for operator of ∆+ = Averaged quantities are defined as: Nx −1 f R ≡ lim 2π lim Nw →+∞ Nx →+∞ i=1 dγi 2π Nw −1 j=1 2π dδj f 2π If we are interested in isotropic local Gaussian disorder: N = Nx = Nw , Ai = Bj = k0 N and k(ξ) = q(ξ) = ξ π k0 N 13 / 15 Cold planar horizons are floppy What about AdS4 ? Disorder in AdS4 : One periodic source does not do, what about many? Nx −1 Nw −1 Φs (x, w, 0) = 2V¯ Ai Bj cos[k(i) x + γi ] cos[q(j) w + λj ] , i=1 j=1 where γi and λj are random phases, and Φs is the source for operator of ∆+ = Averaged quantities are defined as: Nx −1 f R ≡ lim 2π lim Nw →+∞ Nx →+∞ i=1 dγi 2π Nw −1 j=1 2π dδj f 2π If we are interested in isotropic local Gaussian disorder: N = Nx = Nw , Ai = Bj = k0 N and k(ξ) = q(ξ) = ξ π k0 , N in which case: Φ R = 0, and Φs (x, w, 0)Φs (s, h, 0) R = V¯ δ(x − s)δ(w − h) 13 / 15 Cold planar horizons are floppy What about AdS4 ? Results: Example of a fully 3D backreacted run 14 / 15 Cold planar horizons are floppy What about AdS4 ? Results: Example of a fully 3D backreacted run Contour plot of Φ 14 / 15 Cold planar horizons are floppy What about AdS4 ? Results: Example of a fully 3D backreacted run Contour plot of Φ Common questions: 14 / 15 Cold planar horizons are floppy What about AdS4 ? Results: Example of a fully 3D backreacted run Contour plot of Φ Common questions: Since the pointwise value of |Φ| √ grows likes N , why don’t you form black holes bound states? 14 / 15 Cold planar horizons are floppy What about AdS4 ? Results: Example of a fully 3D backreacted run Contour plot of Φ Common questions: Since the pointwise value of |Φ| √ grows likes N , why don’t you form black holes bound states? Is the boundary data regular enough for this problem to be well posed, as N → +∞? 14 / 15 Cold planar horizons are floppy What about AdS4 ? Results: Example of a fully 3D backreacted run 1.030 Contour plot of Φ 1.025 1.020 Common questions: z Since the pointwise value of |Φ| √ grows likes N , why don’t you form black holes bound states? 1.015 1.010 1.005 Is the boundary data regular enough for this problem to be well posed, as N → +∞? gab R 1.000 0.00 0.05 0.10 V 0.15 0.20 is accurately described by a Lifshitz geometry: ds2 R = L2 dt2 − 2(¯z−1) + dx2 + dw2 + dy y y 14 / 15 Cold planar horizons are floppy Conclusion & Outlook Conclusions: Numerical evidence that AdS2 × R2 is RG unstable Instability does not affect AdS4 Disorder potentials affect AdS4 15 / 15 Cold planar horizons are floppy Conclusion & Outlook Conclusions: Numerical evidence that AdS2 × R2 is RG unstable Instability does not affect AdS4 Disorder potentials affect AdS4 What to ask me after the talk: What about more general deformations? Is there a full function of two variables worth of deformations? What are the implications of this IR to transport? 15 / 15 Cold planar horizons are floppy Conclusion & Outlook Conclusions: Numerical evidence that AdS2 × R2 is RG unstable Instability does not affect AdS4 Disorder potentials affect AdS4 What to ask me after the talk: What about more general deformations? Is there a full function of two variables worth of deformations? What are the implications of this IR to transport? Outlook: Can these new IR geometries affect time dependence? Can we make a connection with glassy physics? 15 / 15 ... solutions is 2D: A0 and k0 ≡ kL /¯ µ / 15 Cold planar horizons are floppy Breakdown of Perturbation theory An infamous solution: / 15 Cold planar horizons are floppy Breakdown of Perturbation theory... perturbation theory / 15 Cold planar horizons are floppy Breakdown of Perturbation theory A tale of two resummations: Preserving AdS2 × R2 : / 15 Cold planar horizons are floppy Breakdown of Perturbation.. .Cold planar horizons are floppy Motivation The AdS/CFT correspondence maps asymptotically AdS solutions of Einsteins’ equations to states of a dual conformal field theory / 15 Cold planar horizons