9608117 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year has witnessed a new shift of equal proportions: perturbative ten-dimensional superstrings have in their turn been superseded by a new non-perturbative theory called M-theory, which describes supermembranes and superfivebranes, which subsumes all five consistent string theories and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 S/Z2×K3 (heterotic/heterotic duality) or S1×K3 (Type IIA/heterotic duality) or S/Z2 × T 4 (heterotic/Type IIA duality) or S × T 4 (Type IIA/Type IIA duality). Based on talks given at the Geometry and Physics Conference, Warwick, U. K., March 1996; the SUSY 96 conference, Maryland, U.S.A., June 1996; the CERN Duality Workshop, Geneva, Switzerland, June 1996; and the International School of Subnuclear Physics, Erice, Italy, July 1996. Research supported in part by NSF Grant PHY-9411543. 1 Ten to eleven: it is not too late The maximum spacetime dimension in which one can formulate a consisistent supersymmetric theory is eleven. For this reason in the early 1980’s many physicists looked to D = 11 supergravity [2], in the hope that it might provide that superunification [3] they were all looking for. Then in 1984 superunification underwent a major paradigm shift: eleven-dimensional supergravity was knocked off its pedestal by ten-dimensional superstrings [4], and eleven dimensions fell out of favor. This last year, however, has witnessed a new shift of equal proportions: perturbative ten-dimensional superstrings have in their turn been superseded by a new non-perturbative theory called M-theory, which describes (amongst other things) supersymmetric extended objects with two spatial dimensions (supermembranes), and five spatial dimensions (superfivebranes), which subsumes all five consistent string theories and whose low energy limit is, ironically, eleven-dimensional supergravity. The reason for this reversal of fortune of eleven dimensions is due, in large part, to the 1995 paper by Witten [5]. One of the biggest problems with D = 10 string theory [4] is that there are five consistent string theories: Type I SO(32), heterotic SO(32), heterotic E8×E8, Type IIA and Type IIB. As a candidate for a unique theory of everything, this is clearly an embarrassment of riches. Witten put forward a convincing case that this distinction is just an artifact of perturbation theory and that non-perturbatively these five theories are, in fact, just different corners of a deeper theory. Moreover, this deeper theory, subsequently dubbed M-theory, has D = 11 supergravity as its low energy limit! Thus the five string theories and D = 11 supergravity represent six different special points in the moduli space of M-theory. The small parameters of perturbative string theory are provided by < e >, where Φ is the dilaton field, and < ei > where σi are the moduli fields which arise after compactification. What makes M-theory at once intriguing and yet difficult to analyse is that in D = 11 there is neither dilaton nor moduli and hence the theory is intrinsically non-perturbative. Consequently, the ultimate meaning of M-theory is still unclear, and Witten has suggested The field-theoretic reason is based on the prejudice that there be no massless particles with spins greater than two [1]. However, as discussed in section (5), D = 11 emerges naturally as the maximum dimension admitting super p-branes in Minkowski signature. Some authors take the phrase M -theory to refer merely to this sixth corner of the moduli space. With this definition, of course, M -theory is no more fundamental than the other five corners. For us, M -theory means the whole kit and caboodle.