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

g=1 for Dirichlet 0-branes

Dirichlet 0-branes, considered as extreme Type IIA black holes with spin carried by fermionic hair, are shown to have the anomalous gyromagnetic ratio g=1, consistent with their interpretation as Kaluza-Klein modes.Comment: 13 pages, Late

How fundamental are fundamental constants?

I argue that the laws of physics should be independent of one's choice of units or measuring apparatus. This is the case if they are framed in terms of dimensionless numbers such as the fine structure constant, alpha. For example, the Standard Model of particle physics has 19 such dimensionless parameters whose values all observers can agree on, irrespective of what clock, rulers, scales... they use to measure them. Dimensional constants, on the other hand, such as h, c, G, e, k..., are merely human constructs whose number and values differ from one choice of units to the next. In this sense only dimensionless constants are "fundamental". Similarly, the possible time variation of dimensionless fundamental "constants" of nature is operationally well-defined and a legitimate subject of physical enquiry. By contrast, the time variation of dimensional constants such as c or G on which a good many (in my opinion, confusing) papers have been written, is a unit-dependent phenomenon on which different observers might disagree depending on their apparatus. All these confusions disappear if one asks only unit-independent questions. We provide a selection of opposing opinions in the literature and respond accordingly.Comment: Note added. 30 pages latex. 7 figures. arXiv admin note: text overlap with arXiv:hep-th/0208093 (unpublished

Four Dimensional String/String/String Triality

In six spacetime dimensions, the heterotic string is dual to a Type $IIA$ string. On further toroidal compactification to four spacetime dimensions, the heterotic string acquires an SL(2,\BbbZ)_S strong/weak coupling duality and an SL(2,\BbbZ)_T \times SL(2,\BbbZ)_U target space duality acting on the dilaton/axion, complex Kahler form and the complex structure fields $S,T,U$ respectively. Strong/weak duality in $D=6$ interchanges the roles of $S$ and $T$ in $D=4$ yielding a Type $IIA$ string with fields $T,S,U$. This suggests the existence of a third string (whose six-dimensional interpretation is more obscure) that interchanges the roles of $S$ and $U$. It corresponds in fact to a Type $IIB$ string with fields $U,T,S$ leading to a four-dimensional string/string/string triality. Since SL(2,\BbbZ)_S is perturbative for the Type $IIB$ string, this $D=4$ triality implies $S$-duality for the heterotic string and thus fills a gap left by $D=6$ duality. For all three strings the total symmetry is SL(2,\BbbZ)_S \times O(6,22;\BbbZ)_{TU}. The O(6,22;\BbbZ) is {\it perturbative} for the heterotic string but contains the conjectured {\it non-perturbative} SL(2,\BbbZ)_X, where $X$ is the complex scalar of the $D=10$ Type $IIB$ string. Thus four-dimensional triality also provides a (post-compactification) justification for this conjecture. We interpret the $N=4$ Bogomol'nyi spectrum from all three points of view. In particular we generalize the Sen-Schwarz formula for short multiplets to include intermediate multiplets also and discuss the corresponding black hole spectrum both for the $N=4$ theory and for a truncated $S$--$T$--$U$ symmetric $N=2$ theory. Just as the first two strings are described by the four-dimensional {\it elementary} and {\it dual solitonic} solutions, so theComment: 36 pages, Latex, 2 figures, some references changed, minor changes in formulas and tables; to appear in Nucl. Phys.

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 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

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 (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