Towards a holographic formulation of cosmology

Transcription

1 Towards a holographic formulation of cosmology Gonzalo Torroba Stanford University Topics in holography, supersymmetry and higher derivatives Mitchell Institute, Texas A&M, April 2013

2 During the last century, Cosmology has seen some of the most spectacular discoveries in the history of Physics big bang inflation Dark energy Accelerated expansion Accelerating universe, both in the far past and future Simplest example: de Sitter universe, a / exp(ht) de Sitter (1917)

3 Fascinating properties of accelerating cosmologies: Event horizons Thermodynamic laws Hawking, Bekenstein, Gibbons,... (70 s) event horizon T = H 1, S = Area 4G N Lead to deep questions in theoretical cosmology: a) describe causal patch or global spacetime? b) stat. mech. origin of horizon thermodynamics? c) microscopic degrees of freedom? S ds ?? Formulate quantum gravity on cosmological spacetimes?!

4 Black holes also have event horizons and obey thermodynamic laws. The study of BHs led to Revolution in understanding quantum gravity in string theory: D-branes and AdS/CFT Polchinski (95); Maldacena (97) Holographic principle! CFT t Hooft (93); Susskind (94) Is holography a general property of quantum gravity? Holographic duality for cosmology?

5 Why expect a holographic description of ds? ds entropy = Area of cosmological horizon Basic mechanism responsible for AdS/CFT also present in de Sitter gravitational redshift E loc = p g 00 E pr M Pl Maldacena

6 To understand this, slice AdS and ds by ds AdS d+1 /ds d ds d+1 /ds d from analytic continuation S d+1 /S d, ds 2 = d 2 +sin 2 d 2 ds 2 d+1 = dr 2 +sinh 2 ( r R )ds2 ds d ds 2 d+1 = dr 2 +sin 2 ( r R )ds2 ds d E loc r R E pr! 0 E loc r R E pr! 0 ds d ds d r Holographic dual: QFT living on dsd Holographic dual: 2 EFTs on dsd Alishahiha, Karch, Silverstein, Tong

7 Our goal: formulate cosmology holographically and determine the degrees of freedom that build up cosmological spacetimes Strategy: generalize AdS/CFT to cosmology V FRW ds 1/R AdS

8 A. Uplifting AdS/CFT to cosmology AdS/CFT duality Dong, Horn, Silverstein, GT R B R > 0 X AdS color branes r V B (dr/dr) 2 R 2 =+ 1 R 2 g 2 s N R n 2 R > 0 1/R R > 0 color flux AdS color flux

9 Uplifting AdS/CFT V R < 0 orientifold color flux ds 1/R R > 0 AdS Internal space of negative curvature obtained by adding magnetic flavor branes (more on this below) Orientifolds provide negative tension for the intermediate term in the potential With other ingredients in place to stabilize all light fields... can lead to metastable de Sitter solutions Concrete brane construction given in Dong, Horn, Silverstein, GT arxiv:

10 Brane construction Background internal geometry: (dr/dr) 2 R < 0 R 2 = 1 R 2 + const R d? orientifold N color branes B R < 0 N color antibranes The cone of AdS/CFT now becomes compact Two tips; place color branes at one and antibranes at the other Agrees w/ macroscopics! ds d+1 B Two large N QFTs on dsd plus Gravityd ds/ds

11 Properties of the duality Two large N EFTs living on ds, at finite temperature EFTs coupled to each other at E 1/R ds. Semiholographic: lower dimensional dynamical gravity. But screened by large N matter sector T =1/R ds Microscopic explanation of ds entropy Area of ds Thermal entropy of horizon = large N matter sector parametric count uplifing ingredients subleading FRW decays Dong, Horn, Matsuura Silverstein, GT arxiv: Dual to two t-dep QFTs Precise duality at late times! S!1, GR d decouples

12 B. Magnetic flavors and cosmology Consider AdS 5 S 5 from N D3 branes (p,q) 7 branes compete with internal curvature Wrap AdS 5 3 Large tension T 1 1 R 2 gs 2 V R arxiv: Dong, Horn, Matsuura Silverstein, GT 36 here n R 2, n n 7 n n<0 : AdS n 0 : Cosmology color branes magnetic flavors Dual gauge theory w/ dyonic matter flavor branes Seiberg,Witten; Banks, Douglas, Seiberg; Aharony et al; Polchinski, Silverstein No static sols, but... controlled t-dep FRW sols FRW holography

13 n<0vs n>0 in dual QFT? n<0 can be traced to a unitarity bound E.g. in Seiberg-Witten theory, Dim(u) 1 ) N flavors < 12 So in the static theory n>0 would violate unitarity. Cannot happen in UV complete QFT! Instead, hitting the unitarity bound ) sector of theory becoming free possible transition away from CFT phase However, for n>0 there is a consistent gravity solution well-defined t-dep holographic dual What happens to RG and unitarity bounds in QFTs with spacetime dependent couplings?

14 RG and unitarity bounds in spacetime dependent QFT Intuition: S = S CFT + Z d d x 0 x O arxiv: Dong, Horn, Silverstein, GT Dim(O) = at 0 =0 Power counting: Dim 0 = d + ) relevant for d Tractable class of theories: semiholographic model Z S = S CFT d d x 1 2 (@ )2 + m Z d d xg(x)o Large N sector at g =0, Dim(O) = d 2 + i) Static: Dim(g) =1 irrelevant for > 1 ii) Spacetime dep: g(x) =g 0 x relevant for > 1

15 At large N, effectively gaussian... even with g(x)! g(x) =g 0 x > > 1 Energy = + hooi hooi hooi UV completions Landau pole (x) composite of gauge theory (e.g. SQCD) E g0 g 1 x Infrared nonadiabatic effects h (x) (x 0 )i 1 g(x) x x 0 d 2 g(x 0 )... corrections at very late times Dim( )= d + 2 Translation breaking but new approx. scale invariant fixed point!

16 C. RG structure of ds dual arxiv: Dong, Horn, Silverstein, GT Conditions on a QFT so that it can describe holographically an observer patch of de Sitter? From gravity side, both AdS and ds look very special... n maximal symmetry ) ds 2 d+1 = dr 2 + a(r) 2 ds 2 ds d a(r) = sin(h)(r) for (A)dS moduli stabilization V 0 ( )=0 metastable stable For AdS, properties should be equivalent to having a CFT Features of ds dual that encode max. sym. and stabilization?

17 n n n de Boer, Verlinde, Verlinde; Henningson, Skenderis... Holographic RG Energy-Radius relation: ds 2 = dr 2 + a(r) 2 ĝ µ dx µ dx ) E loc = a(r)e proper E UV QFT RG scale a(r) E L E =0 r =0 r = L r = L UV Z Z QFT = DM e S QF T = Z Z DM E<EL DM E>EL e S QF T = Z bulk = Z Z D Z D e S = Z D r<l e S r<l D r>l e S r>l e S eff(e L ) IR(L, ) Z DM E<EL e S 0(M)+ R d d x p g O Z e S eff(e L ) = e S 0 D e R d d x p g O UV (L, ) Postulate: IR(L, ) = UV (L, ) Heemskerk Polchinski

18 Consequences of moduli stabilization Bulk scalar sitting at (local) minimum: V 0 ( )=0 S = Z, d d+1 x p g (@ ) 2 + V ( )+... V ( )=V V 00 ( ) UV dominated by classical trajectory (L UV )=! (L) = ) log UV has no linear term in Wilson action S e = S 0 (M)+g 1 O g 2(L)O Single trace couplings do not L g 1 =0 2. Iterative structure of L g n only depends on g m<n Strong simplification of RG evolution Suggests new way of organizing the QFT path integral!

19 D. Summary and future directions ds and FRW dual to two EFTs plus gravity; brane construction and ds/ds. Parametric explanation of entropy. matter content: magnetic flavors, uplifiting, unitarity. t-dep, RG and shifts in unitarity bounds special properties of ds dual; moduli stabilization and max. sym. Strong simplification of RG. Nontrivial agreement between micro and macroscopic results indicates a consistent framework for holographic cosmology

20 Future directions Develop more string theory constructions of ds and FRW Explicit description of matter content and couplings of dual QFTs class of QFTs dual to de Sitter Is uplifting the only mechanism for obtaining a ds dual? Relation to global ds/cft description? Reorganization of path integral according to holographic RG meaning of radial cutoff structure of beta functions New critical phenomena from spacetime dependent couplings physical generalization of Wilson-Fisher in integer dimensions applications to controlled models of high Tc superconductors Thank you!