Anti-de Sitter space, branes, singletons, superconformal field theories and all that

Abstract

There has recently been a revival of interest in anti de-Sitter space (AdS) brought about by the conjectured duality beteeen physics in the bulk of AdS and a conformal field theory on the boundary. Since the whole subject of branes, singletons and superconformal field theories on the AdS boundary was an active area of research about ten years ago, I begin with a historical review, including the ``Membrane at the end of the universe'' idea. Next I discuss two recent papers with Lu and Pope on on $Ad{S}_5\times S^5$ and on $Ad{S}_3\times S^3$, respectively. In each case we note that odd-dimensional spheres $S^{2n+1}$ may be regarded as U(1) bundles over $C{P}^n$ and that this permits an unconventional ``Hopf''duality along the U(1) fibre. This leads in particular to the phenomenon of BPS without BPS whereby states which appear to be non-BPS in one picture are seen to be BPS in the dual picture.

Minor improvements. 37 pages Latex. Based on talks delivered at the the PASCOS 98 conference, Northeastern University, March 1998; the Superfivebranes and Physics in 5+1 Dimensions conference, ICTP, Trieste, Italy, April 1998; the Arnowitt Fest, Texas A&M University, April 1998; the Strings 98 conference, ITP, Santa Barbara, June 1998

References in corpus (16)

• Wilson loops in large N field theories
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• AdS3 Black Holes and a Stringy Exclusion Principle
• On Conformal Theories in Four Dimensions
• String Theory and Classical Absorption by Threebranes
• World Volume Approach to Absorption by Non-dilatonic Branes
• Absorption by Branes and Schwinger Terms in the World Volume Theory
• On N=8 Supergravity on $Ad{S}_5$ and N=4 Superconformal Yang-Mills theory
• Spectrum of Large N Gauge Theory from Supergravity
• Duality and asymptotic geometries
• Supersymmetry without Supersymmetry
• G/H M-branes and AdS_{p+2} Geometries
• Special Conformal Symmetry of Worldvolume Actions
• Brane intersections, anti-de Sitter spacetimes and dual superconformal theories
• Branes and anti-de Sitter spacetimes

Cited by in corpus (21)

• Embedding AdS Black Holes in Ten and Eleven Dimensions
• Landscape of superconducting membranes
• D-branes on AdS flux compactifications
• Universal properties of superconformal OPEs for 1/2 BPS operators in $3\le D\le 6$
• Twisted Cohomotopy implies twisted String structure on M5-branes
• Real ADE-equivariant (co)homotopy and Super M-branes
• Conformal primaries of OSp(8/4,R) and BPS states in AdS4
• Global half-BPS $Ad{S}_2\times S^6$ solutions in Type IIB
• Supercoherent States of OSp(8*|2N), Conformal Superfields and the AdS_7/CFT_6 Duality
• Near-horizon brane-scan revived
• The membrane at the end of the (de Sitter) universe
• Geodesic motion in R- charged black hole space-times
• Scalar Multiplet Recombination at Large N and Holography
• (Generalized) Conformal Quantum Mechanics of 0-Branes and Two-Dimensional Dilaton Gravity
• Saturating the unitarity bound in AdS/CFT_(AdS)
• The Search for the Origins of M Theory : Loop Quantum Mechanics, Loops/Strings and Bulk/Boundary Dualities
• Non-BPS Dirac-Born-Infeld Solitons
• Holographic M-Brane Super-Embeddings
• Conformally coupled supermultiplets in four and five dimensions
• Super Fivebranes near the boundary of $Ad{S}_7\times S^4$
• Curvature relations in almost product manifolds