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M-Theory from the Superpoint

Emergence170208

M-Theory from the

M-Theory from the Superpoint John Huerta ∗ , Urs Schreiber † February 8, 2017 Abstract The “brane scan” classifies consistent Green–Schwarz strings and membranes in terms of the invariant cocycles on super-Minkowski spacetimes. The “brane bouquet” generalizes this by consecutively forming the invariant higher central extensions induced by these cocycles, which yields the complete brane content of string/M-theory, including the D-branes and the M5- brane, as well as the various duality relations between these. This raises the question whether the super-Minkowski spacetimes themselves arise as maximal invariant central extensions. Here we prove that they do. Starting from the simplest possible super-Minkowski spacetime, the superpoint, which has no Lorentz structure and no spinorial structure, we give a systematic process of consecutive maximal invariant central extensions, and show that it discovers the super- Minkowski spacetimes that contain superstrings, culminating in the 10- and 11-dimensional super-Minkowski spacetimes of string/M-theory and leading directly to the brane bouquet. Contents 1 Introduction 2 2 Automorphisms of super-Minkowski spacetimes 9 3 The consecutive maximal invariant central extensions of the superpoint 11 4 Outlook 16 A Background 17 A.1 Super Lie algebra cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 A.2 Super Minkowski spacetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 ∗ CAMGSD, Instituto Superior Técnico, Av. Ravisco Pais, 1049-001 Lisboa, Portugal † Mathematics Institute of the Academy, Žitna 25, 115 67 Praha 1, Czech Republic, on leave at Bonn 1

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