1. AdS4/CFT3+gravity for Accelerating Conical Singularities arXiv:0809.2789 arXiv:0809.2789 Mohamed Anber HET Bag Lunch Novemberr 12th

2. 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

3. AdS/CFT: overview Holography (Bekenstein, Susskind, ‘t Hooft, Bousso): information in the bulk is encoded on a surface

4. 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)

5. 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

6. 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 geometryCFT correctionsSemiclassical gravity

7. Gravity in 2+1 D Gravity is not dynamical in 2+1 D Vacuum Solution: conical singularity, no BH

8. 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

9. Geometry of accelerating particles in 2+1 D The presence of point particles in the accelerating frame with conical singularity acceleration

10. Geometry of accelerating particles in 2+1 D The acceleration has to be provided by a strut strut particle

11. 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)

12. Quantum corrections: weakly coupled CFT -Transparent BCs -Dirichlet BCs Strut position

13. Backreaction from weakly coupled CFT: accelerating BH Semiclassical solution Before quantum corrections After quantum corrections: accelerating black hole Regular at the strut

14. Backreaction from weakly coupled CFT: accelerating BH naked singularity!

15. Strongly coupled CFT: the AdS construction The AdS-C metric stringsingularity horizon AdS boundary empty brane

16. 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

17. Strongly coupled CFT: the AdS construction

18. Accelerating BH on the brane, what is the story? Weak CFTStrong CFT classical geometry quantum corrections backreaction AdS+brane Before quantum corrections before=after Position of the string after=? Mass of the string after=? ? coordinate transformation

19. Accelerating BH on the brane, what is the story? To compare the two solutions we use

20. Accelerating BH on the brane, what is the story?

21. Phase transition?

22. 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?

23. Thank you