By Olivier Biquard

Considering that its discovery in 1997 by way of Maldacena, AdS/CFT correspondence has turn into one of many best matters of curiosity in string conception, in addition to one of many major assembly issues among theoretical physics and arithmetic. at the actual facet, it offers a duality among a concept of quantum gravity and a box idea. The mathematical counterpart is the relation among Einstein metrics and their conformal obstacles. The correspondence has been intensively studied, and many growth emerged from the disagreement of viewpoints among arithmetic and physics. Written by means of prime specialists and directed at learn mathematicians and theoretical physicists in addition to graduate scholars, this quantity provides an summary of this crucial region either in theoretical physics and in arithmetic. It comprises survey articles giving a vast evaluation of the topic and of the most questions, in addition to extra really expert articles offering new perception either at the Riemannian aspect and at the Lorentzian aspect of the speculation. A book of the ecu Mathematical Society. disbursed in the Americas by way of the yankee Mathematical Society.

**Read or Download AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries PDF**

**Best differential geometry books**

**Differential Geometry: Theory and Applications (Contemporary Applied Mathematics)**

This publication offers the elemental notions of differential geometry, corresponding to the metric tensor, the Riemann curvature tensor, the basic types of a floor, covariant derivatives, and the basic theorem of floor idea in a self-contained and obtainable demeanour. even supposing the sphere is frequently thought of a classical one, it has lately been rejuvenated, because of the manifold purposes the place it performs an important function.

**Compactifications of Symmetric and Locally Symmetric Spaces (Mathematics: Theory & Applications)**

Introduces uniform structures of lots of the recognized compactifications of symmetric and in the community symmetric areas, with emphasis on their geometric and topological buildings particularly self-contained reference aimed toward graduate scholars and study mathematicians attracted to the functions of Lie thought and illustration idea to research, quantity idea, algebraic geometry and algebraic topology

**An Introduction to Multivariable Analysis from Vector to Manifold**

Multivariable research is a crucial topic for mathematicians, either natural and utilized. except mathematicians, we predict that physicists, mechanical engi neers, electric engineers, platforms engineers, mathematical biologists, mathemati cal economists, and statisticians engaged in multivariate research will locate this publication super valuable.

- Notes on Geometry
- Geometric Analysis and Function Spaces (Cbms Regional Conference Series in Mathematics)
- Compactification of Symmetric Spaces
- Exterior Differential Systems and Equivalence Problems

**Extra info for AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries **

**Example text**

Funct. Anal. 2 (1992), 29–89. [3] M. Anderson, L2 curvature and volume renormalization for AHE metrics on 4-manifolds, Math. Res. Lett. 8 (2001), 171–188. [4] M. Anderson, Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds, Adv. Math. 179 (2003), 205–249. [5] M. DG/0105243. [6] M. Anderson, Some results on the structure of conformally compact Einstein metrics, preprint, Feb. DG/0402198. [7] M. DG/0303260. [8] M . Anderson, Remarks on evolution of spacetimes in 3 + 1 and 4 + 1 dimensions, Classical Quantum Gravity 18 (2001), 5199–5209.

Starting from Lorentzian configurations, one can build configurations with multiple boundary components by taking a 2-dimensional slice of global AdS3 , cutting and gluing it along geodesics and then letting it evolve in time [2]. Such constructions lead, in agreement with the topological censorship theorem, to space-times with the same number h of boundaries and horizons, and with any number g of handles behind the horizons. In the special case where there are only two boundaries (h = 2, g = 0), the space-time describes the eternal BTZ black hole.

217 (2001), 595–622. [23] R. Dijkgraaf, J. Maldacena, G. Moore and E. Verlinde, A black hole farey tail, hepth/0005003. [24] R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero-energy states, J. High Energy Phys. 06 (1999), 036. [25] R. Emparan, C. Johnson and R. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999), 104001. [26] C. Epstein, An asymptotic volume formula for convex cocompact hyperbolic manifolds, in: Appendix A, The divisor of Selberg’s zeta function for Kleinian groups, by S.