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63
Curvature singularities: The good, the bad, and the naked
 Adv. Theor. Math. Phys
, 2002
"... Necessary conditions are proposed for the admissibility of singular classical solutions with 3 + 1dimensional Poincaré invariance to fivedimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain ..."
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Cited by 99 (7 self)
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Necessary conditions are proposed for the admissibility of singular classical solutions with 3 + 1dimensional Poincaré invariance to fivedimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain bounded above for a solution to be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem. In AdS/CFT [1, 2, 3] (see [4] for a review), bulk geometries which are only asymptotically AdS5 near the timelike boundary are dual to relevant deformations of the CFT or to nonconformal vacua. Far from the timelike boundary, various singularities might arise. There must be some restrictions on the type of singularity which is allowed: for
Ricciflat metrics, harmonic forms and brane resolutions hepth/0012011. 9
"... We discuss the geometry and topology of the complete, noncompact, Ricciflat Stenzel metric, on the tangent bundle of Sn+1. We obtain explicit results for all the metrics, and show how they can be obtained from firstorder equations derivable from a superpotential. We then provide an explicit const ..."
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Cited by 95 (19 self)
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We discuss the geometry and topology of the complete, noncompact, Ricciflat Stenzel metric, on the tangent bundle of Sn+1. We obtain explicit results for all the metrics, and show how they can be obtained from firstorder equations derivable from a superpotential. We then provide an explicit construction for the harmonic selfdual (p,q)forms in the middle dimension p + q = 2(n + 1) for the Stenzel metrics in 2(n + 1) dimensions. Only the (p,p)forms are L2normalisable, while for (p,q)forms the degree of divergence grows with p − q. We also construct a set of Ricciflat metrics whose level surfaces are U(1) bundles over a product of N EinsteinKähler manifolds, and we construct examples of harmonic forms there. As an application, we construct new examples of supersymmetric nonsingular fractional M2branes with such 8dimensional transverse Ricciflat spaces. We show explicitly that the fractional D3branes on the 6dimensional Stenzel metric found by Klebanov and Strassler is supported by a pure (2,1)form, and thus it is supersymmetric, while the example of Pando ZayasTseytlin is supported by a mixture of (1,2) and (2,1) forms. We comment on the implications for the corresponding dual field theories of our resolved brane solutions. Contents 1
Brane resolution through transgression
 Nucl. Phys. B
, 2001
"... Modifications to the singularity structure of D3branes that result from turning on a flux for the RR and NSNS 3forms (fractional D3branes) provide important gravity duals of fourdimensional N = 1 superYangMills theories. We construct generalisations of these modified pbrane solutions in a v ..."
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Cited by 37 (14 self)
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Modifications to the singularity structure of D3branes that result from turning on a flux for the RR and NSNS 3forms (fractional D3branes) provide important gravity duals of fourdimensional N = 1 superYangMills theories. We construct generalisations of these modified pbrane solutions in a variety of other cases, including heterotic 5branes, dyonic strings, M2branes, D2branes, D4branes and type IIA and type IIB strings, by replacing the flat transverse space with a Ricciflat manifold Mn that admits covariantly constant spinors, and turning on a flux built from a harmonic form in Mn, thus deforming the original solution and introducing fractional branes. The construction makes essential use of the ChernSimons or “transgression ” terms in the Bianchiidentity or equation of motion of the field strength that supports the original undeformed solution. If the harmonic form is L2 normalisable, this can result in a deformation of the brane solution that is free of singularities, thus providing viable gravity duals of field theories in diverse dimensions that have less than maximal supersymmetry. We obtain examples of nonsingular heterotic 5branes, dyonic strings, M2branes, type IIA strings, and D2branes.
Pope “Consistent warpedspace KaluzaKlein reductions, halfmaximal gauged supergravities and CIP n constructions”, Nucl. Phys. B597
, 2001
"... We obtain new consistent KaluzaKlein embeddings of the gauged supergravities with half of maximal supersymmetry in dimensions D = 7, 6, 5 and 4. They take the form of warped embeddings in type IIA, type IIB, Mtheory and type IIB respectively, and are obtained by performing KaluzaKlein circle redu ..."
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Cited by 34 (5 self)
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We obtain new consistent KaluzaKlein embeddings of the gauged supergravities with half of maximal supersymmetry in dimensions D = 7, 6, 5 and 4. They take the form of warped embeddings in type IIA, type IIB, Mtheory and type IIB respectively, and are obtained by performing KaluzaKlein circle reductions or Tduality transformations on Hopf fibres in S3 submanifolds of the previouslyknown sphere reductions. The new internal spaces are in some sense “mirror manifolds ” that are dual to the original internal spheres. The vacuum AdS solutions of the gauged supergravities then give rise to warped products with these internal spaces. As well as these embeddings, which have singularities, we also construct new nonsingular warped KaluzaKlein embeddings for the D = 5 and D = 4 gauged supergravities. The geometry of the internal spaces in these cases leads us to study FubiniStudy metrics on complex projective spaces in some detail.
de Sitter space from warped supergravity solutions
"... The solutions of 10 and 11 dimensional supergravity that are warped products of de Sitter space with a noncompact ‘internal ’ space are investigated. A convenient form of the metric is found and it is shown that in each case the internal space is asymptotic to a cone over a product of spheres. A co ..."
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Cited by 34 (2 self)
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The solutions of 10 and 11 dimensional supergravity that are warped products of de Sitter space with a noncompact ‘internal ’ space are investigated. A convenient form of the metric is found and it is shown that in each case the internal space is asymptotic to a cone over a product of spheres. A consistent truncation gives gauged supergravities with noncompact gauge groups. The BPS domain wall solutions of the noncompact gauged supergravities are lifted to warped solutions in 10 or 11 dimensions. 1. NonCompact Gaugings and Higher Dimensional Solutions Gauged supergravities with compact gauge groups typically arise from dimensional reduction of higher dimensional supergravities with compact internal spaces. In [1], it was shown that the supergravities with noncompact gauge groups are associated with higher dimensional supergravity solutions that have a noncompact ‘internal ’ space. In particular, de Sitter space solutions in D = 4, 5 arise in this way. The nogo theorems of [2,3] imply that de Sitter space cannot arise form a compactification of a higherdimensional supergravity theory, and the solutions of
Lü and C.N. Pope Domain Walls with Localised Gravity and Domain Wall/QFT correspondence hepth/0007209
"... We review general domainwall solutions supported by a deltafunction source, together with a single pure exponential scalar potential in supergravity. These scalar potentials arise from a sphere reduction in Mtheory or string theory. There are several examples of flat (BPS) domain walls that lead ..."
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Cited by 19 (3 self)
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We review general domainwall solutions supported by a deltafunction source, together with a single pure exponential scalar potential in supergravity. These scalar potentials arise from a sphere reduction in Mtheory or string theory. There are several examples of flat (BPS) domain walls that lead to a localisation of gravity on the brane, and for these we obtain the form of the corrections to Newtonian gravity. These solutions are lifted back on certain internal spheres to D = 11 and D = 10 as Mbranes and Dbranes. We find that the domain walls that can trap gravity yield Mbranes or Dpbranes that have a natural decoupling limit, i.e. p ≤ 5, with the deltafunction source providing an ultraviolet cutoff in a dual quantum field theory. This suggests that the localisation of gravity can generally be realised within a Domainwall/QFT correspondence, with the deltafunction domainwall source providing a cutoff from the spacetime boundary for these domainwall solutions. We also discuss the form of the oneloop corrections to the graviton propagator from the boundary QFT that would reproduce the corrections to the Newtonian gravity on the domain wall.
Gravity duals for the Coulomb branch of marginally deformed
 N = 4 YangMills,” hepth/0510132
"... deformed N = 4 YangMills ..."
Geometry of the embedding of supergravity scalar manifolds
 in D = 11 and D
"... Several recent papers have made considerable progress in proving the existence of remarkable consistent KaluzaKlein sphere reductions of D = 10 and D = 11 supergravities, to give gauged supergravities in lower dimensions. A proof of the consistency of the full gauged SO(8) reduction on S7 from D = ..."
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Cited by 9 (2 self)
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Several recent papers have made considerable progress in proving the existence of remarkable consistent KaluzaKlein sphere reductions of D = 10 and D = 11 supergravities, to give gauged supergravities in lower dimensions. A proof of the consistency of the full gauged SO(8) reduction on S7 from D = 11 was given many years ago, but from a practical viewpoint a reduction to a smaller subset of the fields can be more manageable and explicit, for the purposes of lifting lowerdimensional solutions back to the higher dimension. The major complexity of the spherical reduction Ansätze comes from the spin0 fields, and of these, it is the pseudoscalars that are the most difficult to handle. In this paper we address this problem in two cases. One arises in a truncation of SO(8) gauged supergravity in four dimensions to U(1) 4, where there are three pairs of dilatons and axions in the scalar sector. The other example involves the truncation of SO(6) gauged supergravity in D = 5 to a subsector containing a scalar and a pseudoscalar field, with a potential that admits a second supersymmetric vacuum aside from the maximallysupersymmetric one. We briefly discuss the use of these embedding Ansätze for the lifting of solutions back to the higher dimension.
Consistent Sphere Reductions and Universality of the Coulomb Branch in the DomainWall/QFT Correspondence
, 2000
"... We prove that any Ddimensional theory comprising gravity, an antisymmetric nindex field strength and a dilaton can be consistently reduced on Sn in a truncation in which just n scalar fields and the metric are retained in (D − n)dimensions, provided only that the strength of the couping of the di ..."
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Cited by 8 (3 self)
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We prove that any Ddimensional theory comprising gravity, an antisymmetric nindex field strength and a dilaton can be consistently reduced on Sn in a truncation in which just n scalar fields and the metric are retained in (D − n)dimensions, provided only that the strength of the couping of the dilaton to the field strength is appropriately chosen. A consistent reduction can then be performed for n ≤ 5; with D being arbitrary when n ≤ 3, whilst D ≤ 11 for n = 4 and D ≤ 10 for n = 5. (Or, by Hodge dualisation, n can be replaced by (D −n) in these conditions.) We obtain the lower dimensional scalar potentials and construct associated domain wall solutions. We use the consistent reduction Ansatz to lift domainwall solutions in the (D − n)dimensional theory back to D dimensions, where we show that they become certain continuous distributions of (D − n − 2)branes. We also examine the spectrum for a minimallycoupled scalar field in the domainwall background, showing that it has a universal structure characterised completely by the dimension n of the compactifying sphere.