Download Adventures with Superstrings

Andrew
Chamblin
Memorial
Louisville
March 22, 2006
Thermal Properties of Strongly Coupled Gauge Theories
with Fundamental Matter from Gauge/Gravity Duality
(Inflation in the AdS/CFT)
Freivogel, Hubeny, Maloney, RCM, Rangamani and Shenker
(hep-th/0510046)
Anti-de Sitter space does not inflate!
0
How do we study inflation with AdS/CFT?
“Attach” AdS space to an inflating region
String Theory Landscape:
string theory seems to yield “landscape” with many,
many “vacua” with Λ positive, negative or zero
Simple model for landscape:
V
dS
^
0
1
^
AdS ~ CFT
• fluctuations around 1 are captured in CFT
extends to excursions to dS extremum at 0
• study bubbles of dS phase in AdS background
(closely related to “creating a universe in a laboratory”)
Farhi & Guth; Farhi, Guth & Guven
domain
wall
1
1
0
0
Thin wall approximation:
R
small
g ab smooth at boundary but  n g ab discontinuous
AdS:   1
use Israel boundary conditions:
Tab   (r ) Sab
dS:   0


ab  K ab
 K ab
ab  g ab  cc  8 G Sab
 8 G g ab
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:
• AdS radius:
• Bubble mass:
• BH horizon:
where
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:
• effective particle motion with
dimensionless
radius
bubble mass
microscopic
parameters
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
inside
cut and paste:
Schwarzschild-AdS space
outside
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 regions
always arise behind BH horizon (Einstein-Rosen throat)
(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
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)
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,
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.?
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]
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
quantum tunnelling
classical
“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!!
quantum mechanics: pure
X
initial small bubble = pure state
“target” inflating solution = mixed state
mixed
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??
So long, my friend.