Louisville March 22, 2006

1. Andrew Chamblin Memorial Louisville March 22, 2006 Thermal Properties of Strongly Coupled Gauge Theories with Fundamental Matter from Gauge/Gravity Duality An AdS (Inflation in the AdS/CFT)

2. Freivogel, Hubeny, Maloney, RCM, Rangamani and Shenker (hep-th/0510046) Anti-de Sitter space does not inflate! How do we study inflation with AdS/CFT? “Attach” AdS space to an inflating region

3. String Theory Landscape: string theory seems to yield “landscape” with many, many “vacua” with Λ positive, negative or zero

4. Simple model for landscape: V dS ^ ^ AdS ~ CFT • fluctuations around are captured in CFT extends to excursions to dS extremum at • study bubbles of dS phase in AdS background (closely related to “creating a universe in a laboratory”) Farhi & Guth; Farhi, Guth & Guven

5. domain wall Thin wall approximation: small smooth at boundary but discontinuous AdS: use Israel boundary conditions: dS:

6. Thin domain wall constructions: Other simplifications: spherically symmetric; 4 dimensions Metric inside bubble: de Sitter space Metric outside bubble: Schwarzschild-AdS space Scales: • dS radius: where • AdS radius: • Bubble mass: • BH horizon:

7. Thin domain wall constructions: • geometries are patched together at domain wall: • world-volume metric: • wall trajectory determined by junction condition: extrinsic curvatures ~ • calculate, calculate, calculate …….. effective classical mechanics problem

8. dimensionless radius Thin domain wall constructions: • effective particle motion with bubble mass microscopic parameters

9. Thin domain wall constructions: • effective particle motion with

10. Thin domain wall constructions: • effective particle motion with

11. Thin domain wall constructions: • effective particle motion with

12. Thin domain wall constructions: Penrose diagrams: de Sitter space Schwarzschild-AdS space

13. Thin domain wall constructions: Penrose diagrams: de Sitter space Schwarzschild-AdS space inside outside cut and paste:

14. Thin domain wall constructions:

15. Thin domain wall constructions:

16. Thin domain wall constructions:

17. Thin domain wall constructions:

18. Thin domain wall constructions: singularity

19. Thin domain wall constructions:

20. Thin domain wall constructions:

21. Thin domain wall constructions:

22. Boundary CFT / Holography: • light collapsing dS bubbles: excitations of AdS vacuum • which are described by boundary CFT • inflating dS bubbles?

23. Boundary CFT / Holography: • light collapsing dS bubbles: excitations of AdS vacuum • which are described by boundary CFT • inflating dS bubbles:claim these are not described by • CFT alone – new holographic d.o.f. describe dS region central to argument is observation that inflating regions always arise behind BH horizon (Einstein-Rosen throat)

24. (Maldacena; Balasubramanian etal) Detour on AdS/CFT correspondence: • eternal Schwarzschild-AdS space corresponds to • pure entangled state in doubled Hilbert space • tracing over leaves mixed state in right CFT

25. Detour on AdS/CFT correspondence: • eternal Schwarzschild-AdS space corresponds to • pure entangled state in doubled Hilbert space • tracing over leaves mixed state in right CFT • radial cut-off in AdS, • energy cut-off in CFT, geodesics with higher energies probe AdS space out to larger radius [ plus (D – 1)-dimensional gravity! ] (Randall & Sundrum)

26. Holography and Inflating Bubbles: • consider • large region on left appears as Schwarzschild-AdS • introduce cut-off : only Sch.-AdS!! have entangled state in two independent cut-off CFT’s • as increases: fill out CFT on right, • higher-E d.o.f. not organized as CFT but • still large independent dual,

27. Holography and Inflating Bubbles: • consider • independent holographic d.o.f. needed to describe • inflating dS bubble on left!! • may have pure entangled state on two Hilbert spaces • or mixed state on single Hilbert space of CFT on right What can we say about new holographic d.o.f.?

28. Detour back to Eternal AdS Black Hole: Fidkowski, Hubeny, Kleban & Shenker • boundary operators with large dimension Δ describe bulk • particles with mass m ~ Δ • black hole singularity repells • geodesics certain correlators • contain singularity when geodesic • becomes null [singularity is off in complex plane]

29. Probes of Inflation in AdS/CFT: • same probe for entangled state of AdS and dS bubble • “big crunch” singularities do not repell geodesics • extinguishes singularities for certain ranges

30. “Creating a universe in a laboratory” (Farhi & Guth) • classically creating inflating region requires past singularity singularity theorems p

31. “Creating a universe in a laboratory” (Farhi & Guth) • classically creating inflating region requires past singularity singularity theorems (Farhi, Guth & Guven) • quantum tunnelling could lead to creation of inflating region classical classical quantum tunnelling

32. “Creating a universe in a laboratory” (Farhi & Guth) • classically creating inflating region requires past singularity singularity theorems (Farhi, Guth & Guven) • quantum tunnelling could lead to creation of inflating region no euclidean instanton!! “pseudo-instanton”? • unitarity of quantum mechanics prevents process!! initial small bubble = pure state “target” inflating solution = mixed state X quantum mechanics: pure mixed

33. Discussion: • string theory seems to yield landscape • with many AdS & dS “vacua” • while AdS described by CFT, AdS connected to • inflating region requires additional holographic d.o.f. tracing out dS d.o.f. results in mixed state for CFT • have controlled framework to study dS holography nearly null geodesics give dramatic effects in CFT correlators (on second sheet) • cannot “build” inflating universe, even quantum mechanically • other questions/answers? precisely when does holographic dual make transition from pure to mixed state??

34. So long, my friend.