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AdS4/CFT3+gravity for Accelerating
Conical Singularities arXiv:0809.2789
Mohamed AnberHET Bag Lunch
Novemberr 12th
Outline
AdS/CFT:overview AdS/CFT+gravity Gravity in 2+1 D Geometry of accelerating particles in 2+1 D Quantum corrections: weakly coupled CFT Backreaction from weakly coupled CFT: accelerating BH Strongly coupled CFT: the AdS construction Accelerating BH on the brane, what is the story? conclusion
AdS/CFT: overview
Holography (Bekenstein, Susskind, ‘t Hooft, Bousso): information in the bulk is encoded on a surface
D
s G
SL
4)(EntropyD
AdS/CFT: overview
AdS space: Solution to Einstein’s equations with negative cosmological constant
Conformal Field theory (CFT): Invariant under conformal transformations=Poincaré +scale invariance, Roughly speaking for odd dimensions
Maldacena conjecture (AdS/CFT) (1997)0
T
AdS/CFT+gravity
Extra Dimensions!! Kaluza–Klein compactification Randall-Sundrum model: large extra dimensions (brane
) On the RS brane: gravity+CFT(UV cutoff ) Provides a natural set up to study strongly coupled CFT
systems in non-trivial gravitational backgrounds
5~ 5AdS
AdS/CFT+gravity
Black holes (BH) localized on RS-branes: BH evaporation (classical BH+CFT corrections)
Important for quantum gravity But no localized BH on RS 3-brane (4+1 D bulk) so far!! Emparan, Horowitz and Myers (EHM) (1999) found BHs
on RS 2-brane (3+1 D bulk) Emparan, Fabbri and Kaloper interpretation: (EHM) BHs
are quantum corrected BHs. How they did it?
They compared the quantum corrections to a point mass in 2+1 D to (EHM) BHs
Classical geometry CFT corrections Semiclassical gravity
Gravity in 2+1 D
Gravity is not dynamical in 2+1 D Vacuum Solution: conical singularity, no BH
00
RG
20
22222 drdrdtds
Gravity in 2+1 D
Why to study accelerating conical singularities? It provides a natural setup for a CFT kept at a finite
temperature (Unruh effect) The presence of acceleration horizon may give us some
idea about the more interesting case of BHs on the RS 3-brane.
Finite temperature CFT: a clue about a possible confinement/de-confinement phase transition
Geometry of accelerating particles in
2+1 D
The presence of point particles in the accelerating frame
with conical singularity
with conical singularity
acceleration
Geometry of accelerating particles in
2+1 D
The acceleration has to be provided by a strut
strut particle
Quantum corrections: weakly coupled CFT
Lagrangian density Conformally coupled theory Acceleration finite temperature (Unruh effect) Euclidean time thermal Green’s function
To find the quantum corrections to the classical spacetime:
1-solve for well behaved with appropriate BCs
2- regularize by subtracting
3-calculate the energy-momentum tensor (Casimir effect)
Quantum corrections: weakly coupled CFT
-Transparent BCs
-Dirichlet BCs
Strut position
Backreaction from weakly coupled CFT: accelerating BH
Semiclassical solution
Before quantum corrections
After quantum corrections: accelerating black hole
Regular at the strut
Backreaction from weakly coupled CFT: accelerating BH
naked singularity!
Strongly coupled CFT: the AdS construction
The AdS-C metric
stringsingularity
horizonAdS boundary
empty brane
Strongly coupled CFT: the AdS construction
Compute the extrinsic curvature Write down the Israel junction condition
The induced metric on the brane
induced metric
K-
K+n
Accelerating BH dressed with strongly coupled CFT
Strongly coupled CFT: the AdS construction
Accelerating BH on the brane, what is the story?
Weak CFT Strong CFT
classical geometry quantum corrections
backreactionAdS+brane
Before quantum corrections
before= after
Position of the string after=?Mass of the string after=?
?
coordinate transformation
Accelerating BH on the brane, what is the story?
To compare the two solutions we use
Accelerating BH on the brane, what is the story?
Accelerating BH on the brane, what is the story?
Phase transition?
conclusion AdS/CFT+gravity to understand strongly coupled CFT in
non-tervial backgrounds More to understand about the number of degrees of
freedom in strongly coupled CFT (suppressed? Why? What implications for the absent BH on the RS-3 brane?)
Can we learn about realistic systems?
Thank you