ads4/cft3+gravity for accelerating conical singularities arxiv:0809.2789 arxiv:0809.2789 mohamed...
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AdS4/CFT3+gravity for Accelerating
Conical Singularities arXiv:0809.2789
Mohamed AnberHET Bag Lunch
Novemberr 12th
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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
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AdS/CFT: overview
Holography (Bekenstein, Susskind, ‘t Hooft, Bousso): information in the bulk is encoded on a surface
D
s G
SL
4)(EntropyD
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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
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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
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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
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Gravity in 2+1 D
Gravity is not dynamical in 2+1 D Vacuum Solution: conical singularity, no BH
00
RG
20
22222 drdrdtds
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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
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Geometry of accelerating particles in
2+1 D
The presence of point particles in the accelerating frame
with conical singularity
with conical singularity
acceleration
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Geometry of accelerating particles in
2+1 D
The acceleration has to be provided by a strut
strut particle
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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)
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Quantum corrections: weakly coupled CFT
-Transparent BCs
-Dirichlet BCs
Strut position
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Backreaction from weakly coupled CFT: accelerating BH
Semiclassical solution
Before quantum corrections
After quantum corrections: accelerating black hole
Regular at the strut
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Backreaction from weakly coupled CFT: accelerating BH
naked singularity!
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Strongly coupled CFT: the AdS construction
The AdS-C metric
stringsingularity
horizonAdS boundary
empty brane
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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
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Strongly coupled CFT: the AdS construction
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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
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Accelerating BH on the brane, what is the story?
To compare the two solutions we use
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Accelerating BH on the brane, what is the story?
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Accelerating BH on the brane, what is the story?
Phase transition?
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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?
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Thank you