M-Theory (The theory formerly known as Strings)Superunification underwent a major paradigm shift in 1984 when eleven-dimensional supergravity was knocked off its pedestal by ten-dimensional superstrings. This last year has witnessed a new shift of equal proportions: perturbative ten-dimensional superstrings have in their turn been superseded by a new non-perturbative theory called M-theory, which describes supermembranes and superfivebranes, which subsumes all five consistent string theories and whose low energy limit is, ironically, eleven-dimensional supergravity. In particular, six-dimensional string/string duality follows from membrane/fivebrane duality by compactifying M-theory on S1/Z2 ×K3 (heterotic/heterotic duality) or S1 ×K3 (Type IIA/heterotic duality) or S1/Z2 × T 4 (heterotic/Type IIA duality) or S1 × T 4 (Type IIA/Type IIA duality).
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Multi-Membrane Solutions of D = 11 SupergravityWe find exact solutions to the field equations of eleven-dimensional supergravity corresponding to stable multi-membrane configurations. Their holonomy group is given by the SO (8) subgroup of an enlarged tangent space group SO ( l, 2 ) × SO (16), and hence one half of the spacetime supersymmetries are broken. The solutions saturate a Bogomol'nyi bound between the mass per unit area and the Page charge, which also guarantees their stability.
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Superstrings in D=10 from Supermembranes in D=11The type IIA superstring in ten dimensions is derived from the supermembrane in eleven dimensions by a simultaneous dimensional reduction of the world volume and the spacetime.
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Thirty years of Erice on the brane |
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After initially meeting with fierce resistance, branes, p-dimensional extended objects which go beyond particles (p = 0) and strings (p = 1), now occupy centre stage in the- oretical physics as microscopic components of M-theory, as the seeds of the AdS/CFT correspondence, as a branch of particle phenomenology, as the higher-dimensional pro- genitors of black holes and, via the brane-world, as entire universes in their own right. Notwithstanding this early opposition, Nino Zichichi invited me to to talk about su- permembranes and eleven dimensions at the 1987 School on Subnuclear Physics and has continued to keep Erice on the brane ever since. Here I provide a distillation of my Erice brane lectures and some personal recollections.