M. J. Duff

Embedding AdS black holes in ten and eleven dimensions

Abstract We construct the non-linear Kaluza-Klein ansatze describing the embeddings of the U (1) 3 , U (1) 4 and U (1) 2 truncations of D = 5, D = 4 and D = 7 gauged supergravities into the type IIB string and M-theory. These enable one to oxidise any associated lower-dimensional solutions to D = 10 or D = 11. In particular, we use these general ansatze to embed the charged AdS 5 , AdS 4 and AdS 7 black hole solutions in ten and eleven dimensions. The charges for the black holes with toroidal horizons may be interpreted as the angular momenta of D3-branes, M2-branes and M5-branes spinning in the transverse dimensions, in their near-horizon decoupling limits. The horizons of the black holes coincide with the world-volumes of the branes. The Kaluza-Klein ansatze also allow the black holes with spherical or hyperbolic horizons to be reinterpreted in D = 10 or D = 11.

Eleven-dimensional origin of string/string duality: a one-loop test☆

Abstract Membrane/ fivebrane duality in D = 11 implies Type IIA string/Type IIA fivebrane duality in D = 10, which in turn implies Type HA string/heterotic string duality in D = 6. To test the conjecture, we reproduce the corrections to the 3-form field equations of the D = 10 Type IIA string (a mixture of tree-level and one-loop effects) starting from the Chern-Simons corrections to the 7-form Bianchi identities of the D = 11 fivebrane (a purely tree-level effect). K3 compactification of the latter then yields the familiar gauge and Lorentz Chem-Simons corrections to 3-form Bianchi identities of the heterotic string. We note that the absence of a dilaton in the D = 11 theory allows us to fix both the gravitational constant and the fivebrane tension in terms of the membrane tension. We also comment on an apparent conflict between fundamental and solitonic heterotic strings and on the puzzle of a fivebrane origin of S -duality.

Twenty years of the Weyl anomaly

In 1973 two Salam proteges (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor displayed by classical massless-field systems in interaction with gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black-hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic review.

Duality rotations in string theory

Abstract Global non-compact symmetries of four-dimensional string theories have their origin in duality transformations on the world-sheet which rotate field equations into Bianchi identities. Starting from a σ-model with target space coordinates x μ ( μ = 1,…, n ), we introduce a dual σ-model with coordinates y α ( α = 1,…, n ) for which the roles of field equations and Bianchi identities are interchanged. The hidden symmetries are then made manifest by considering a target space of double the dimension with coordinates Z M = ( x μ , y α ).

Non-local conformal anomalies

The vacuum polarization by external gauge fields of conformally invariant quantum field systems is shown to manifest a new, non-local, type of trace anomaly when gauge-invariant dimensional regularisation is used. Examples include neutrino and photon loops in a background metric gravitational field and charged massles fermion loops in background metric and electromagnetic fields.

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

Black and super p-branes in diverse dimensions

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ANTI-DE SITTER BLACK HOLES IN GAUGED N = 8 SUPERGRAVITY

-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

Quantum Inequivalence of Different Field Representations

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EVIDENCE FOR HETEROTIC/HETEROTIC DUALITY

-theory on