1996/05/31 by H. Lü, H. Lu, C.N. Pope +3 · 37 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Diagonal #Dimension (graph theory) #Dimensional reduction #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Reduction (mathematics) #Scalar (mathematics) #Supergravity #Symmetry (geometry) #hep-th
paper · pdf · doi:10.1016/s0550-3213(96)90137-6
published in Nuclear Physics B 481(1-2), 313-331 (Elsevier BV) · Latex, 21 pages, no figures. References added
arxiv created 1996/09/16 · openalex publication_date 1996/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In addition to the double-dimensional reduction procedure that employs world-volume Killing symmetries of p-brane supergravity solutions and acts diagonally on a plot of p versus spacetime dimension D, there exists a second procedure of ``vertical'' reduction. This reduces the transverse-space dimension via an integral that superposes solutions to the underlying Laplace equation. We show that vertical reduction is also closely related to the recently-introduced notion of intersecting p-branes. We illustrate this with examples, and also construct a new D=11 solution describing four intersecting membranes, which preserves 1/16 of the supersymmetry. Given the two reduction schemes plus duality transformations at special points of the scalar modulus space, one may relate most of the p-brane solutions of relevance to superstring theory. We argue that the maximum classifying duality symmetry for this purpose is the Weyl group of the corresponding Cremmer-Julia supergravity symmetry Er(+r). We also discuss a separate class of duality-invariant p-branes with p=D-3.