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