Ja n 20 15 IMPERIAL-TP-2014-MJD-06 M-history without the M 1

A review of the book “A Brief History of String Theory: From Dual Models to M-Theory” by Dean Rickles. Prior to the 1984 superstring revolution, most theoretical physicists paid little attention to the work of Green and Schwarz on ten-dimensional superstrings. Many preferred supergravity in eleven dimensions, the maximum dimension permitted by supersymmetry of the elementary particles. So one can sympathise with John Schwarz when he complains in the book that this pioneering work went largely unrecognised until 1984. However, most string theorists were in their turn slow to recognise the importance of membranes and eleven dimensions. There are no superstrings in eleven dimensions but, as was shown in 1987, there are supermembranes [1, 2, 3], which is why between 1984 and 1995 many string theorists were opposed to eleven dimensions. Membrane-related grant proposals tended to attract hostile referee reports during that period and papers with titles like “Supermembranes: a fond farewell” did not help. One string theorist announced that “I want to cover up my ears every time I hear the word membrane” and some organisers of the annual superstring conferences even banned the use of the “M-word”. My colleague Paul Townsend, one of the membrane pioneers, compared this with the theatrical superstition of calling Macbeth the “M-Play”. This opposition continued even after it was shown in 1987 that one of the five consistent ten-dimensional superstring theories, the Type IIA string, was just the limiting case of the eleven-dimensional supermembrane [4] and even after it was shown in 1994 that the spectrum of states that resulted from compactifying the membrane theory from eleven dimensions to four was identical to that resulting from compactifying the Type IIA string from ten dimensions to four [5, 6]. Commissioned by Contemporary Physics. DOI:10.1080/00107514.2014. 992964 m.duff@imperial.ac. uk However, attitudes to eleven dimensions among both string and membrane theorists underwent a sea-change in March 1995 when string-guru Edward Witten, drawing on work by Hull and Townsend, Sen and myself, made an astonishing announcement at the Strings 95 conference in Los Angeles. The five consistent strings (1, IIA, IIB, HE, HO) were not, as previously thought, five rival candidates for the final theory but were merely five corners of a deeper and more profound eleven-dimensional structure [7], which he called M-theory. The ultraviolet divergences of D = 11 supergravity are now seen to be irrelevant because it is just the low-energy approximation to the underlying M-theory. Curiously, however, Witten did not immediately embrace membranes even then: There is, for instance, no evidence for membrane excitations; such evidence might well have appeared if a consistent membrane theory with eleven-dimensional supergravity as its low energy limit really does exist [8]. It has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it M-theory, leaving for future the relation of M to membranes [9]. However, it soon became clear that the equations of M-theory in diverse dimensions less than or equal to eleven admit solutions describing a variety of “p-branes”, with a web of “dualities” relating them. (Here a 0-brane is a point-particle, a 1-brane is a string, a 2-brane is a membrane and so on.) Prior to these developments, string calculations had to rely on “perturbation theory”, an approximation that involves keeping just the first few terms in an expansion in powers of some small parameter g. But the importance of these dualities was that they permitted for the first time non-perturbative calculations, relating a theory with parameter g to another with parameter 1/g. While remaining open-minded about the fundamental degrees of freedom of M-theory, Witten was soon converted to the utility of membranes and went on to make contributions to membrane theory as profound as those he had made to string theory. October 1995 marked another major development in the history of membranes and M-theory when Joe Polchinksi [10] observed that a subset of the p-brane solutions to D = 10 Type IIA and Type IIB supergravities admit the alternative interpretation of Dirichlet-branes (or Dp-branes): surfaces of dimension p on which open strings can end. Importantly for the purposes of this review, since D-branes may be framed within the language of ten dimensional superstrings they were psychologically more palatable to those who had opposed eleven dimensional membranes which were then renamed M-branes. Thus the “electric” D = 11 membrane becomes the M2-brane, and its “magnetic” dual the M5-brane. D-branes had profound implications. For example, when combined with the M-branes, they led to Juan Maldacena’s AdSd/CFT correspondence which conjectured a remarkable equivalence between gravitational theories living in d-dimensional spacetimes of the saddle-shaped anti-de Sitter (AdS) variety and non-gravitational conformal field theories (CFT) living on their (p = d − 2)-dimensional boundaries. Maldacena’s paper, which focussed on AdS4/M2-branes, AdS5/D3-branes and AdS7/M5-branes, has garnered an incredible > 10, 000 citations. D-branes