arXiv subjects

M. J. Duff

Publications and source records attributed to M. J. Duff.

At least 91 records · Page 5Linked to original sources

arXiv2001

Hodge Duality on the Brane

It has been claimed that whereas scalars can be bound to a Randall-Sundrum brane, higher p-form potentials cannot, in contradiction with the Hodge duality between 0-form and 3-form potentials in the five-dimensional bulk. Here we show that a 3-form in the bulk correctly yields a 2-form on the brane, in complete agreement with both bulk and brane duality. We also emphasize that the phenomenon of photon screening in the Randall-Sundrum geometry is ruled out by the bulk Einstein equation.

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arXiv2001

Localization of supergravity on the brane

A supersymmetric Randall-Sundrum brane-world demands that not merely the graviton but the entire supergravity multiplet be trapped on the brane. To demonstrate this, we present a complete ansatz for the reduction of (D=5,N=4) gauged supergravity to (D=4,N=2) ungauged supergravity in the Randall-Sundrum geometry. We verify that it is consistent to lowest order in fermion terms. In particular, we show how the graviphotons avoid the `no photons on the brane' result because they do not originate from Maxwell's equations in D=5 but rather from odd-dimensional self-duality equations. In the case of the fivebrane, the Randall-Sundrum mechanism also provides a new Kaluza-Klein way of obtaining chiral supergravity starting from non-chiral.

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arXiv2001

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.

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arXiv2000

Randall-Sundrum Brane Tensions

We show that the singular sources in the energy-momentum tensor for the Randall-Sundrum brane world, viewed as a solution of type IIB supergravity, are composed of two elements. One of these is a D3-brane source with tension opposite in sign to the RS tension in five dimensions; the other arises from patching two regions of flat ten-dimensional spacetime. This resolves an apparent discrepancy between supersymmetry and the sign and magnitude of the RS tension.

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arXiv2000

A supersymmetric Type IIB Randall-Sundrum realization

We show that an earlier domain wall solution of type IIB supergravity provides a supersymmetric realization of the Randall-Sundrum brane-world, and give its ten-dimensional interpretation in terms of IIB 3-branes. We also explain how previous no-go theorems are circumvented. In particular, whereas D=5 supergravity scalars have AdS_5 energy E_0 <= 4 and are unable to support a D=5 positive tension brane, our scalar has E_0=8, and is the breathing mode of the S^5 compactification. Another essential element of the construction is the implementation of a Z_2 symmetry by patching together compactifications with opposite signs for their 5-form field strengths. This is thus a IIB analogue of a previous D=5 3-brane realization of the Horava-Witten orbifold. A mode-locking phenomenon avoids the appearance of negative energy zero-modes in spite of the necessity of a D=10 negative tension brane-source.

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arXiv2000

Complementarity of the Maldacena and Randall-Sundrum Pictures

We revive an old result, that one-loop corrections to the graviton propagator induce 1/r^3 corrections to the Newtonian gravitational potential, and compute the coefficient due to closed loops of the U(N) {\cal N}=4 super-Yang-Mills theory that arises in Maldacena's AdS/CFT correspondence. We find exact agreement with the coefficient appearing in the Randall-Sundrum brane-world proposal. This provides more evidence for the complementarity of the two pictures.

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arXiv2000

TASI Lectures on Branes, Black Holes and Anti-de Sitter Space

In the light of the duality between physics in the bulk of anti-de Sitter space and a conformal field theory on the boundary, we review the M2, D3 and M5 branes and how their near-horizon geometry yields the compactification of D=11 supergravity on S^{7}, Type IIB supergravity on S^{5} and D=11 supergravity on S^{4}, respectively. We discuss the ``Membrane at the End of the Universe'' idea and its relation to the corresponding superconformal singleton theories that live on the boundary of the AdS_{4}, AdS_{5} and AdS_{7} vacua. The massless sectors of these compactifications are described by the maximally supersymmetric D=4, D=5 and D=7 gauged supergravities. We construct the non-linear Kaluza-Klein ansätze describing the embeddings of the U(1)^4, U(1)^3 and U(1)^2 truncations of these supergravities, which admit 4-charge AdS_{4}, 3-charge AdS_{5} and 2-charge AdS_{7} black hole solutions. These enable us to embed the black hole solutions back in ten and eleven dimensions and reinterpret them as M2, D3 and M5 branes spinning in the transverse dimensions with the black hole charges given by the angular momenta of the branes. A comprehensive Appendix lists the field equations, symmetries and transformation rules of D=11 supergravity, Type IIB supergravity, and the M2, D3 and M5 branes.

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arXiv1999

Embedding AdS Black Holes in Ten and Eleven Dimensions

We construct the non-linear Kaluza-Klein ansätze 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 ansätze 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 tranverse dimensions, in their near-horizon decoupling limits. The horizons of the black holes coincide with the worldvolumes of the branes. The Kaluza-Klein ansätze also allow the black holes with spherical or hyperbolic horizons to be reinterpreted in D=10 or D=11.

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arXiv1999

Anti-de Sitter Black Holes in Gauged N=8 Supergravity

We present new anti-de Sitter black hole solutions of gauged N=8, SO(8) supergravity, which is the massless sector of the AdS_4\times S^7 vacuum of M-theory. By focusing on the U(1)^4 Cartan subgroup, we find non-extremal 1, 2, 3 and 4 charge solutions. In the extremal limit, they may preserve up to 1/2, 1/4, 1/8 and 1/8 of the supersymmetry, respectively. In the limit of vanishing SO(8) coupling constant, the solutions reduce to the familiar black holes of the M_4\times T^7 vacuum, but have very different interpretation since there are no winding states on S^7 and no U-duality. In contrast to the T^7 compactification, moreover, we find no static multi-center solutions. Also in contrast, the S^7 fields appear "already dualized" so that the 4 charges may be all electric or all magnetic rather than 2 electric and 2 magnetic. Curiously, however, the magnetic solutions preserve no supersymmetries. We conjecture that a subset of the extreme electric black holes preserving 1/2 the supersymmetry may be identified with the S^7 Kaluza-Klein spectrum, with the non-abelian SO(8) quantum numbers provided by the fermionic zero modes.

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arXiv1999

A Lattice Universe from M-theory

A recent paper on the large-scale structure of the Universe presented evidence for a rectangular three-dimensional lattice of galaxy superclusters and voids, with lattice spacing ~120 Mpc and called for some ``hitherto unknown process'' to explain it. Here we report that a rectangular three-dimensional lattice of intersecting domain walls, with arbitrary spacing, emerges naturally as a classical solution of M-theory.

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arXiv1998

Anti-de Sitter space, branes, singletons, superconformal field theories and all that

There has recently been a revival of interest in anti de-Sitter space (AdS) brought about by the conjectured duality beteeen physics in the bulk of AdS and a conformal field theory on the boundary. Since the whole subject of branes, singletons and superconformal field theories on the AdS boundary was an active area of research about ten years ago, I begin with a historical review, including the ``Membrane at the end of the universe'' idea. Next I discuss two recent papers with Lu and Pope on on $AdS_{5} \times S^{5}$ and on $AdS_{3} \times S^{3}$, respectively. In each case we note that odd-dimensional spheres $S^{2n+1}$ may be regarded as U(1) bundles over $CP^{n}$ and that this permits an unconventional ``Hopf''duality along the U(1) fibre. This leads in particular to the phenomenon of BPS without BPS whereby states which appear to be non-BPS in one picture are seen to be BPS in the dual picture.

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arXiv1998

AdS_3 x S^3 (Un)twisted and Squashed, and an O(2,2;Z) Multiplet of Dyonic Strings

We consider type IIB configurations carrying both NS-NS and R-R electric and magnetic 3-form charges, and whose near horizon geometry contains AdS_3 x S^3. Noting that S^3 is a U(1) bundle over CP^1 \sim S^2, we construct the dual type IIA configurations by a Hopf T-duality along the U(1) fibre. In the case where there are only R-R charges, the S^3 is untwisted to S^2 x S^1 (in analogy with a previous treatment of AdS_5 x S^5.) However, in the case where there are only NS-NS charges, the S^3 becomes the cyclic lens space S^3/Z_p with its round metric (and is hence invariant when p=1), where p is the magnetic NS-NS charge. In the generic case with NS-NS and R-R charges, the S^3 not only becomes S^3/Z_p but is also squashed, with a squashing parameter that is related to the values of the charges. Similar results apply if we regard AdS_3 as a bundle over AdS_2 and T-dualise along the fibre. We show that Hopf T-dualities relate different black holes, and that they preserve the entropy. The AdS_3 x S^3 solutions arise as the near-horizon limits of dyonic strings. We construct an O(2,2;Z) multiplet of such dyonic strings, where O(2,2;Z) is a subgroup of the O(5,5) or O(5,21) six-dimensional duality groups, which captures the essence of the NS-NS/R-R and electric/magnetic dualities.

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arXiv1998

Instanton Cosmology and Domain Walls from M-theory and String Theory

The recent proposal by Hawking and Turok for obtaining an open inflationary universe from singular instantons makes use of low-energy effective Lagrangians describing gravity coupled to scalars and non-propagating antisymmetric tensors. In this paper we derive some exact results for Lagrangians of this type, obtained from spherical compactifications of M-theory and string theory. In the case of the S^7 compactification of M-theory, we give a detailed discussion of the cosmological solutions. We also show that the lower-dimensional Lagrangians admit domain-wall solutions, which preserve one half of the supersymmetry, and which approach AdS spacetimes near their horizons.

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arXiv1998

A Layman's Guide to M-theory

The best candidate for a fundamental unified theory of all physical phenomena is no longer ten-dimensional superstring theory but rather eleven-dimensional {\it M-theory}. In the words of Fields medalist Edward Witten, ``M stands for `Magical', `Mystery' or `Membrane', according to taste''. New evidence in favor of this theory is appearing daily on the internet and represents the most exciting development in the subject since 1984 when the superstring revolution first burst on the scene. (Talk delivered at the Abdus Salam Memorial Meeting, ICTP, Trieste, November 1997.)

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arXiv1998

AdS_5 x S^5 Untwisted

Noting that T-duality untwists S^5 to CP^2 x S^1, we construct the duality chain: n=4 super Yang-Mills --> Type IIB superstring on AdS_5 x S^5 --> Type IIA superstring on AdS_5 x CP^2 x S^1 --> M-theory on AdS_5 x CP^2 x T^2. This provides another example of supersymmetry without supersymmetry: on AdS_5 x CP^2 x S^1, Type IIA supergravity has SU(3) x U(1) x U(1) x U(1) and N=0 supersymmetry but Type IIA string theory has SO(6) and N=8. The missing superpartners are provided by stringy winding modes. We also discuss IIB compactifications to AdS_5 with N=4, N=2 and N=0.

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arXiv1998

Gauge Dyonic Strings and Their Global Limit

We show that six-dimensional supergravity coupled to tensor and Yang-Mills multiplets admits not one but two different theories as global limits, one of which was previously thought not to arise as a global limit and the other of which is new. The new theory has the virtue that it admits a global anti-self-dual string solution obtained as the limit of the curved-space gauge dyonic string, and can, in particular, describe tensionless strings. We speculate that this global model can also represent the worldvolume theory of coincident branes. We also discuss the Bogomol'nyi bounds of the gauge dyonic string and show that, contrary to expectations, zero eigenvalues of the Bogomol'nyi matrix do not lead to enhanced supersymmetry and that negative tension does not necessarily imply a naked singularity.

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arXiv1998

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.

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arXiv1997

The Octonionic Membrane

We generalize the supermembrane solution of D=11 supergravity by permitting the 4-form $G$ to be either self-dual or anti-self-dual in the eight dimensions transverse to the membrane. After analyzing the supergravity field equations directly, and also discussing necessary conditions for unbroken supersymmetry, we focus on two specific, related solutions. The self-dual solution is not asymptotically flat. The anti-self-dual solution is asymptotically flat, has finite mass per unit area and saturates the same mass=charge Bogomolnyi bound as the usual supermembrane. Nevertheless, neither solution preserves any supersymmetry. Both solutions involve the octonionic structure constants but, perhaps surprisingly, they are unrelated to the octonionic instanton 2-form $F$, for which $TrF \wedge F$ is neither self-dual nor anti-self-dual.

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