String and M-theory: answering the critics

Using as a springboard a three-way debate between theoretical physicist Lee Smolin, philosopher of science Nancy Cartwright and myself, I address in layman's terms the issues of why we need a unified theory of the fundamental interactions and why, in my opinion, string and M-theory currently offer the best hope. The focus will be on responding more generally to the various criticisms. I also describe the diverse application of string/M-theory techniques to other branches of physics and mathematics which render the whole enterprise worthwhile whether or not "a theory of everything" is forthcoming.Comment: Update on EPSRC. (Contribution to the Special Issue of Foundations of Physics: "Forty Years Of String Theory: Reflecting On the Foundations", edited by Gerard 't Hooft, Erik Verlinde, Dennis Dieks and Sebastian de Haro. 22 pages latex

State of the Unification Address

After reviewing how M-theory subsumes string theory, I report on some new and interesting developments, focusing on the ``brane-world'': circumventing no-go theorems for supersymmetric brane-worlds, complementarity of the Maldacena and Randall-Sundrum pictures; self-tuning of the cosmological constant. I conclude with the top ten unsolved problems.Comment: 16 pages, Latex. Plenary talk delivered at The Division of Particles and Fields Meeting of The American Physical Society, August 9-12 2000, Ohio State University. Minor corrections and references adde

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year has witnessed a new shift of equal proportions: perturbative ten-dimensional superstrings have in their turn been superseded by a new non-perturbative theory called {\it $M$-theory}, which describes supermembranes and superfivebranes, which subsumes all five consistent string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 $S^1/Z_2 \times K3$ (heterotic/heterotic duality) or $S^1 \times K3$ (Type $IIA$/heterotic duality) or $S^1/Z_2 \times T^4$ (heterotic/Type $IIA$ duality) or $S^1 \times T^4$ (Type $IIA$/Type $IIA$ duality).Comment: Version to appear in I.J.M.P.A. References added; typographical errors corrected; 25 pages Late

Electric/magnetic duality and its stringy origins

We review electric/magnetic duality in $N=4$ (and certain $N=2$) globally supersymmetric gauge theories and show how this duality, which relates strong to weak coupling, follows as a consequence of a string/string duality. Black holes, eleven dimensions and supermembranes also have a part to play in the big picture.Comment: A few minor improvements; 23 pages LaTe

The world in eleven dimensions: a tribute to Oskar Klein

Current attempts to find a unified theory that would reconcile Einstein's General Relativity and Quantum Mechanics, and explain all known physical phenomena, invoke the Kaluza-Klein idea of extra spacetime dimensions. The best candidate is M-theory, which lives in eleven dimensions, the maximum allowed by supersymmetry of the elementary particles. We give a non-technical account. An Appendix provides an updated version of Edwin A. Abbott's 1884 satire {\it Flatland: A Romance of Many Dimensions}. Entitled {\it Flatland, Modulo 8}, it describes the adventures of a superstring theorist, A. Square, who inhabits a ten-dimensional world and is initially reluctant to accept the existence of an eleventh dimension.Comment: Oskar Klein Professorship Inaugural Lecture, University of Michigan, 16 March 2001. 38 pages, Latex, 15 color figure

M-theory on manifolds of G2 holonomy: the first twenty years

In 1981, covariantly constant spinors were introduced into Kaluza-Klein theory as a way of counting the number of supersymmetries surviving compactification. These are related to the holonomy group of the compactifying manifold. The first non-trivial example was provided in 1982 by D=11 supergravity on the squashed S7, whose G2 holonomy yields N=1 in D=4. In 1983, another example was provided by D=11 supergravity on K3, whose SU(2) holonomy yields half the maximum supersymmetry. In 2002, G2 and K3 manifolds continue to feature prominently in the full D=11 M-theory and its dualities. In particular, singular G2 compactifications can yield chiral (N=1,D=4) models with realistic gauge groups. The notion of generalized holonomy is also discussed.Comment: Notes added on n, the number of allowed M-theory supersymmetries. Asymmetric orbifold compactifications of Type II strings from D=10 to D=2 permit n=0,1,2,3,4,5,6,8,9,10,12,16,17,18,20,24,3