arXiv subjects

H. Lu

Publications and source records attributed to H. Lu.

At least 361 records · Page 20Linked to original sources

arXiv2001

Supersymmetric Domain Walls from Metrics of Special Holonomy

Supersymmetric domain-wall spacetimes that lift to Ricci-flat solutions of M-theory admit generalized Heisenberg (2-step nilpotent) isometry groups. These metrics may be obtained from known cohomogeneity one metrics of special holonomy by taking a "Heisenberg limit", based on an Inönü-Wigner contraction of the isometry group. Associated with each such metric is an Einstein metric with negative cosmological constant on a solvable group manifold. We discuss the relevance of our metrics to the resolution of singularities in domain-wall spacetimes and some applications to holography. The extremely simple forms of the explicit metrics suggest that they will be useful for many other applications. We also give new but incomplete inhomogeneous metrics of holonomy SU(3), $G_2$ and Spin(7), which are $T_1$, $T_2$ and $T_3$ bundles respectively over hyper-Kähler four-manifolds.

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arXiv2001

Resolved Branes and M-theory on Special Holonomy Spaces

We review the construction of regular p-brane solutions of M-theory and string theory with less than maximal supersymmetry whose transverse spaces have metrics with special holonomy, and where additional fluxes allow brane resolutions via transgression terms. We focus on the properties of resolved M2-branes and fractional D2-branes, whose transverse spaces are Ricci flat eight-dimensional and seven-dimensional spaces of special holonomy. We also review fractional M2-branes with transverse spaces corresponding to the new two-parameter Spin(7) holonomy metrics, and their connection to fractional D2-branes with transverse spaces of G_2 holonomy.

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arXiv2001

A New Fractional D2-brane, G_2 Holonomy and T-duality

Recently, a new example of a complete non-compact Ricci-flat metric of G_2 holonomy was constructed, which has an asymptotically locally conical structure at infinity with a circular direction whose radius stabilises. In this paper we find a regular harmonic 3-form in this metric, which we then use in order to obtain an explicit solution for a fractional D2-brane configuration. By performing a T-duality transformation on the stabilised circle, we obtain the type IIB description of the fractional brane, which now corresponds to D3-brane with one of its world-volume directions wrapped around the circle.

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arXiv2001

Massless 3-brane in M-theory

We construct supersymmetric M3-brane solutions in D=11 supergravity. They can be viewed as deformations of backgrounds taking the form of a direct product of four-dimensional Minkowski spacetime and a non-compact Ricci-flat manifold of G_2 holonomy. Although the 4-form field strength is turned on it carries no charge, and the 3-branes are correspondingly massless. We also obtain 3-branes of a different type, arising as M5-branes wrapped over S^2.

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arXiv2001

Supersymmetric M3-branes and G_2 Manifolds

We obtain a generalisation of the original complete Ricci-flat metric of G_2 holonomy on R^4\times S^3 to a family with a non-trivial parameter λ. For generic λthe solution is singular, but it is regular when λ={-1,0,+1}. The case λ=0 corresponds to the original G_2 metric, and λ={-1,1} are related to this by an S_3 automorphism of the SU(2)^3 isometry group that acts on the S^3\times S^3 principal orbits. We then construct explicit supersymmetric M3-brane solutions in D=11 supergravity, where the transverse space is a deformation of this class of G_2 metrics. These are solutions of a system of first-order differential equations coming from a superpotential. We also find M3-branes in the deformed backgrounds of new G_2-holonomy metrics that include one found by A. Brandhuber, J. Gomis, S. Gubser and S. Gukov, and show that they also are supersymmetric.

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arXiv2001

New Complete Non-compact Spin(7) Manifolds

We construct new explicit metrics on complete non-compact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by A_8, is topologically R^8 and another, which we denote by B_8, is the bundle of chiral spinors over $S^4$. Unlike the previously-known complete non-compact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S^4, our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP^3. We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of opposite dualities) for the B_8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L^2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A_8 and B_8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In an appendix we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B^+_8 and B^-_8 similar to B_8.

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arXiv2001

Hyper-Kahler Calabi Metrics, L^2 Harmonic Forms, Resolved M2-branes, and AdS_4/CFT_3 Correspondence

We obtain a simple explicit expression for the hyper-Kahler Calabi metric on the co-tangent bundle of CP^{n+1}, for all n, in which it is constructed as a metric of cohomogeneity one with SU(n+2)/U(n) principal orbits. These results enable us to obtain explicit expressions for an L^2-normalisable harmonic 4-form in D=8, and an L^2-normalisable harmonic 6-form in D=12. We use the former in order to obtain an explicit resolved M2-brane solution, and we show that this solution is invariant under all three of the supersymmetries associated with the covariantly-constant spinors in the 8-dimensional Calabi metric. We give some discussion of the corresponding dual N=3 three-dimensional field theory. Various other topics are also addressed, including superpotentials for the Calabi metrics and the metrics of exceptional G_2 and Spin(7) holonomy in D=7 and D=8. We also present complex and quaternionic conifold constructions, associated with the cone metrics whose resolutions are provided by the Stenzel T^*S^{n+1} and Calabi T^*\CP^{n+1} metrics. In the latter case we relate the construction to the hyper-Kahler quotient. We then use the hyper-Kähler quotient to give a quaternionic rederivation of the Calabi metrics.

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arXiv2001

Ricci-flat Metrics, Harmonic Forms and Brane Resolutions

We discuss the geometry and topology of the complete, non-compact, Ricci-flat Stenzel metric, on the tangent bundle of S^{n+1}. We obtain explicit results for all the metrics, and show how they can be obtained from first-order equations derivable from a superpotential. We then provide an explicit construction for the harmonic self-dual (p,q)-forms in the middle dimension p+q=(n+1) for the Stenzel metrics in 2(n+1) dimensions. Only the (p,p)-forms are L^2-normalisable, while for (p,q)-forms the degree of divergence grows with |p-q|. We also construct a set of Ricci-flat metrics whose level surfaces are U(1) bundles over a product of N Einstein-Kahler manifolds, and we construct examples of harmonic forms there. As an application, we construct new examples of deformed supersymmetric non-singular M2-branes with such 8-dimensional transverse Ricci-flat spaces. We show explicitly that the fractional D3-branes on the 6-dimensional 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 Zayas-Tseytlin 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.

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arXiv2001

Supersymmetric Non-singular Fractional D2-branes and NS-NS 2-branes

We obtain regular deformed D2-brane solutions with fractional D2-branes arising as wrapped D4-branes. The space transverse to the D2-brane is a complete Ricci-flat 7-manifold of G_2 holonomy, which is asymptotically conical with principal orbits that are topologically CP^3 or the flag manifold SU(3)/(U(1) x U(1)). We obtain the solution by first constructing an L^2 normalisable harmonic 3-form. We also review a previously-obtained regular deformed D2-brane whose transverse space is a different 7-manifold of G_2 holonomy, with principal orbits that are topologically S^3 x S^3. This describes D2-branes with fractional NS-NS 2-branes coming from the wrapping of 5-branes, which is supported by a non-normalisable harmonic 3-form on the 7-manifold. We prove that both types of solutions are supersymmetric, preserving 1/16 of the maximal supersymmetry and hence that they are dual to {\cal N}=1 three-dimensional gauge theories. In each case, the spectrum for minimally-coupled scalars is discrete, indicating confinement in the infrared region of the dual gauge theories. We examine resolutions of other branes, and obtain necessary conditions for their regularity. The resolution of many of these seems to lie beyond supergravity. In the process of studying these questions, we construct new explicit examples of complete Ricci-flat metrics.

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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

Brane Resolution Through Transgression

Modifications to the singularity structure of D3-branes that result from turning on a flux for the R-R and NS-NS 3-forms (fractional D3-branes) provide important gravity duals of four-dimensional N=1 super-Yang-Mills theories. We construct generalisations of these modified p-brane solutions in a variety of other cases, including heterotic 5-branes, dyonic strings, M2-branes, D2-branes, D4-branes and type IIA and type IIB strings, by replacing the flat transverse space with a Ricci-flat manifold M_n that admits covariantly constant spinors, and turning on a flux built from a harmonic form in M_n, thus deforming the original solution and introducing fractional branes. The construction makes essential use of the Chern-Simons or ``transgression'' terms in the Bianchi-identity or equation of motion of the field strength that supports the original undeformed solution. If the harmonic form is L^2 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 non-singular heterotic 5-branes, dyonic strings, M2-branes, type IIA strings, and D2-branes.

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arXiv2000

Brane-world Kaluza-Klein reductions and Branes on the Brane

We present a systematic study of a new type of consistent ``Brane-world Kaluza-Klein Reduction,'' which describe fully non-linear deformations of co-dimension one objects that arise as solutions of a large class of gauged supergravity theories in diverse dimensions, and whose world-volume theories are described by ungauged supergravities with one half of the original supersymmetry. In addition, we provide oxidations of these Ansatze which are in general related to sphere compactified higher dimensional string theory or M-theory. Within each class we also provide explicit solutions of brane configurations localised on the world-brane. We show that at the Cauchy horizon (in the transverse dimension of the consistently Kaluza-Klein reduced world-brane) there is a curvature singularity for any configuration with a non-null Riemann curvature or a non-vanishing Ricci scalar that lives in the world-brane. Since the massive Kaluza-Klein modes can be consistently decoupled, they cannot participate in regulating these singularities.

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arXiv2000

Branes on the Brane

We show that four-dimensional N=2 ungauged Einstein-Maxwell supergravity can be embedded on the Randall-Sundrum 3-brane, as a consistent Kaluza-Klein reduction of five-dimensional N=4 gauged supergravity. In particular, this allows us to describe four-dimensional Reissner-Nordstrom black holes within the Randall-Sundrum scenario. Using earlier results on the embedding of five-dimensional N=4 gauged supergravity in ten dimensions, we can then describe the four-dimensional Einstein-Maxwell supergravity on the 3-brane, and its solutions, from a type IIB viewpoint. We also show that the minimal ungauged supergravities in D=5 and D=6 can be consistently embedded in the half-maximally supersymmetric gauged supergravities in D=6 and D=7 respectively. These allow us to construct solutions including BPS black holes and strings living in "Randall-Sundrum 4-branes," and BPS self-dual strings living in "Randall-Sundrum 5-branes." We can also lift the embeddings to ten-dimensional massive type IIA and D=11 supergravity respectively. In particular, we obtain a solution describing the self-dual string living in the world-volume of an M5-brane, which can be viewed as an open membrane ending on the M5-brane.

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arXiv2000

Domain Walls with Localised Gravity and Domain-Wall/QFT Correspondence

We review general domain-wall solutions supported by a delta-function source, together with a single pure exponential scalar potential in supergravity. These scalar potentials arise from a sphere reduction in M-theory 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 M-branes and D-branes. We find that the domain walls that can trap gravity yield M-branes or Dp-branes that have a natural decoupling limit, i.e. p\le 5, with the delta-function source providing an ultra-violet cut-off in a dual quantum field theory. This suggests that the localisation of gravity can generally be realised within a Domain-wall/QFT correspondence, with the delta-function domain-wall source providing a cut-off from the space-time boundary for these domain-wall solutions. We also discuss the form of the one-loop corrections to the graviton propagator from the boundary QFT that would reproduce the corrections to the Newtonian gravity on the domain wall.

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arXiv2000

Consistent Warped-Space Kaluza-Klein Reductions, Half-Maximal Gauged Supergravities and CP^n Constructions

We obtain new consistent Kaluza-Klein 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, M-theory and type IIB respectively, and are obtained by performing Kaluza-Klein circle reductions or T-duality transformations on Hopf fibres in S^3 submanifolds of the previously-known 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 non-singular warped Kaluza-Klein embeddings for the D=5 and D=4 gauged supergravities. The geometry of the internal spaces in these cases leads us to study Fubini-Study metrics on complex projective spaces in some detail.

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arXiv2000

S^3 and S^4 Reductions of Type IIA Supergravity

We construct a consistent reduction of type IIA supergravity on S^3, leading to a maximal gauged supergravity in seven dimensions with the full set of massless SO(4) Yang-Mills fields. We do this by starting with the known S^4 reduction of eleven-dimensional supergravity, and showing that it is possible to take a singular limit of the resulting standard SO(5)-gauged maximal supergravity in seven dimensions, whose eleven-dimensional interpretation involves taking a limit where the internal 4-sphere degenerates to RxS^3. This allows us to reinterpret the limiting SO(4)-gauged theory in seven dimensions as the S^3 reduction of type IIA supergravity. We also obtain the consistent S^4 reduction of type IIA supergravity, which gives an SO(5)-gauged maximal supergravity in D=6.

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arXiv2000

AdS in Warped Spacetimes

We obtain a large class of AdS spacetimes warped with certain internal spaces in eleven-dimensional and type IIA/IIB supergravities. The warp factors depend only on the internal coordinates. These solutions arise as the near-horizon geometries of more general semi-localised multi-intersections of $p$-branes. We achieve this by noting that any sphere (or AdS spacetime) of dimension greater than 3 can be viewed as a foliation involving S^3 (or AdS_3). Then the S^3 (or AdS_3) can be replaced by a three-dimensional lens space (or a BTZ black hole), which arises naturally from the introduction of a NUT (or a pp-wave) to the M-branes or the D3-brane. We then obtain multi-intersections by performing a Kaluza-Klein reduction or Hopf T-duality transformation on the fibre coordinate of the lens space (or the BTZ black hole). These geometries provide further possible examples of the AdS/CFT correspondence and of consistent embeddings of lower-dimensional gauged supergravities in D=11 or D=10.

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arXiv2000

Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence

We prove that any D-dimensional theory comprising gravity, an antisymmetric n-index field strength and a dilaton can be consistently reduced on S^n 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\le 5; with D being arbitrary when n\le 3, whilst D\le 11 for n=4 and D\le 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 domain-wall 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 minimally-coupled scalar field in the domain-wall background, showing that it has a universal structure characterised completely by the dimension n of the compactifying sphere.

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