AdS/CFT Correspondence: Einstein Metrics and Their Conformal - download pdf or read online

By Olivier Biquard

ISBN-10: 3037190132

ISBN-13: 9783037190135

In view that its discovery in 1997 via Maldacena, AdS/CFT correspondence has turn into one of many best topics of curiosity in string idea, in addition to one of many major assembly issues among theoretical physics and arithmetic. at the actual aspect, it offers a duality among a conception of quantum gravity and a box idea. The mathematical counterpart is the relation among Einstein metrics and their conformal limitations. The correspondence has been intensively studied, and many growth emerged from the war of words of viewpoints among arithmetic and physics. Written through best specialists and directed at learn mathematicians and theoretical physicists in addition to graduate scholars, this quantity supplies an outline of this crucial quarter either in theoretical physics and in arithmetic. It comprises survey articles giving a wide evaluation of the topic and of the most questions, in addition to extra really good articles supplying new perception either at the Riemannian facet and at the Lorentzian facet of the speculation. A e-book of the ecu Mathematical Society. allotted in the Americas through the yankee Mathematical Society.

Show description

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

Similar differential geometry books

New PDF release: Global Differential Geometry and Global Analysis 1984

All papers showing during this quantity are unique study articles and feature now not been released in other places. They meet the necessities which are precious for e-book in an outstanding caliber fundamental magazine. E. Belchev, S. Hineva: at the minimum hypersurfaces of a in the community symmetric manifold. -N. Blasic, N.

Download e-book for iPad: Geometry, topology, and physics by Mikio Nakahara

This booklet introduces a number of present mathematical tips on how to postgraduate scholars of theoretical physics. this is often completed through proposing functions of the math to physics, high-energy physics, common relativity and condensed topic physics

Get Introduction To Compact Lie Groups PDF

There are ways to compact lie teams: via computation as matrices or theoretically as manifolds with a gaggle constitution. the good attraction of this e-book is the mixing of those ways. The theoretical effects are illustrated by means of computations and the speculation presents a remark at the computational paintings.

J-holomorphic curves and quantum cohomology - download pdf or read online

J$-holomorphic curves revolutionized the learn of symplectic geometry while Gromov first brought them in 1985. via quantum cohomology, those curves are actually associated with a few of the most enjoyable new principles in mathematical physics. This publication offers the 1st coherent and whole account of the idea of $J$-holomorphic curves, the main points of that are shortly scattered in a number of study papers.

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

Example text

For more details, see [8]. 6 The field is constant in the sense that the field strength of the U(1) connection is proportional to the AdS2 volume form. e. wormholes), we must look at configurations which do not satisfy the conditions of the Witten–Yau theorem. One possibility is to look at spaces which have two boundaries, each being a Riemann surface of genus g ≥ 2, g [49]: ds 2 = dρ 2 + cosh2 ρ ds 2 g . (27) The boundaries have constant negative curvature, so the Witten–Yau theorem does not apply here, but unlike in higher dimensions, the two-dimensional field theories on these Riemann surfaces are well-defined and stable.

7) then give ¯ρ ρ ¯ρ ρ + (R − n(n + 1))/ρ 2 ≥ −2n ¯ρ ρ . + (Ricg −ng)(T , T )/ρ 2 . 17) where again φ = − ¯ ρ/ρ. 8) also holds, and hence Rγ < 0 implies φ(0) < 0. 16). 3 to the situation where Rγ = 0. 1, (S, g) has + = ∅ and no time-like geodesic is futurecomplete unless (S, g) is isometric to g = −dt 2 + e2t gN n , where gN n is Ricci-flat, cf. [11] for further details. 15) cannot be geodesically complete if Rγ < 0, and have at most one component of conformal infinity. This exhibits the role of the hypothesis Rγ > 0 in a more drastic way than the AH case.

8), where T = ∇ρ is the future-directed unit vector. We summarize some of this discussion in the following result. 1. 7). 8). This correspondence thus gives a rigorous form of “Wick rotation” between these types of Einstein metrics. The Fefferman–Graham expansion holds for Einstein metrics of any signature (again as observed in [27]). In the correspondence between AH 24 Michael T. 12) where + occurs if k ≡ 0, 1 (mod 4), while − occurs if k ≡ 2, 3 (mod 4). 19) for the renormalized action and its variation also have analogues for dS space-times.

Download PDF sample

AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries by Olivier Biquard


by Jeff
4.4

Rated 4.12 of 5 – based on 37 votes