LouisvilleMarch 22, 2006

AndrewChamblinMemorial

An AdSThermal Properties of Strongly Coupled Gauge Theorieswith Fundamental Matter from Gauge/Gravity Duality

(Inflation in the AdS/CFT)

Anti-de Sitter space does not inflate!

0

How do we study inflation with AdS/CFT?

“Attach” AdS space to an inflating region

Freivogel, Hubeny, Maloney, RCM, Rangamani and Shenker(hep-th/0510046)

string theory seems to yield “landscape” with many,many “vacua” with Λ positive, negative or zero

String Theory Landscape:

01

^^

VSimple model for landscape:

AdS ~ CFT

dS

• fluctuations around are captured in CFT

• study bubbles of dS phase in AdS background

1

(closely related to “creating a universe in a laboratory”)Farhi & Guth; Farhi, Guth & Guven

extends to excursions to dS extremum at 0

11

00

domainwall

Thin wall approximation: smallR

0 dS:

1 AdS:

abab r S)(T use Israel boundary conditions:

ababab KK

ab

abccabab

g

g

G8

SG8

smooth at boundary but discontinuousabgnabg

Thin domain wall constructions:

Other simplifications: spherically symmetric; 4 dimensions

Metric inside bubble:

Metric outside bubble:

• dS radius: where

• AdS radius:

• BH horizon:

• Bubble mass:

Scales:

de Sitter space

Schwarzschild-AdS space

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

Thin domain wall constructions:

bubble mass

• effective particle motion with

microscopicparameters

dimensionlessradius

Thin domain wall constructions:

• effective particle motion with

Thin domain wall constructions:

• effective particle motion with

Thin domain wall constructions:

• effective particle motion with

Thin domain wall constructions:

Penrose diagrams:

de Sitter space Schwarzschild-AdS space

Thin domain wall constructions:

Penrose diagrams:

de Sitter space Schwarzschild-AdS space

cut and paste:

outsideinside

Thin domain wall constructions:

Thin domain wall constructions:

Thin domain wall constructions:

Thin domain wall constructions:

Thin domain wall constructions:

singularity

Thin domain wall constructions:

Thin domain wall constructions:

Thin domain wall constructions:

Boundary CFT / Holography:

• light collapsing dS bubbles: excitations of AdS vacuum which are described by boundary CFT

• inflating dS bubbles?

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 regionsalways arise behind BH horizon (Einstein-Rosen throat)

• tracing over leaves mixed state in right CFT

Detour on AdS/CFT correspondence:

• eternal Schwarzschild-AdS space corresponds to pure entangled state in doubled Hilbert space

(Maldacena; Balasubramanian etal)

• tracing over leaves mixed state in right CFT

Detour on AdS/CFT correspondence:

• eternal Schwarzschild-AdS space corresponds to pure entangled state in doubled Hilbert space

• radial cut-off in AdS, energy cut-off in CFT,

[ plus (D – 1)-dimensional gravity! ] (Randall & Sundrum)

geodesics with higher energiesprobe AdS space out to larger radius

Holography and Inflating Bubbles:

• consider

• large region on left appears as Schwarzschild-AdS• introduce cut-off :

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,

only Sch.-AdS!!

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.?

Fidkowski, Hubeny, Kleban & Shenker

Detour back to Eternal AdS Black Hole:

• 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]

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

“Creating a universe in a laboratory”(Farhi & Guth)

• classically creating inflating region requires past singularity

singularity theorems

p

“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

classicalquantum tunnelling

“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

quantum mechanics: pure mixedX

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 holographynearly 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 maketransition from pure to mixed state??

So long, my friend.