arXiv subjects

H. Lu

Publications and source records attributed to H. Lu.

At least 379 records · Page 21Linked to original sources

arXiv2000

Consistent Kaluza-Klein Sphere Reductions

We study the circumstances under which a Kaluza-Klein reduction on an n-sphere, with a massless truncation that includes all the Yang-Mills fields of SO(n+1), can be consistent at the full non-linear level. We take as the starting point a theory comprising a p-form field strength and (possibly) a dilaton, coupled to gravity in the higher dimension D. We show that aside from the previously-studied cases with (D,p)=(11,4) and (10,5) (associated with the S^4 and S^7 reductions of D=11 supergravity, and the S^5 reduction of type IIB supergravity), the only other possibilities that allow consistent reductions are for p=2, reduced on S^2, and for p=3, reduced on S^3 or S^{D-3}. We construct the fully non-linear Kaluza-Klein Ansatze in all these cases. In particular, we obtain D=3, N=8, SO(8) and D=7, N=2, SO(4) gauged supergravities from S^7 and S^3 reductions of N=1 supergravity in D=10.

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arXiv2000

Consistency of Kaluza-Klein Sphere Reductions of Symmetric Potentials

In a recent paper, the complete (non-linear) Kaluza-Klein Ansatz for the consistent embedding of certain scalar plus gravity subsectors of gauged maximal supergravity in D=4, 5 and 7 was presented, in terms of sphere reductions from D=11 or type IIB supergravity. The scalar fields included in the truncations were the diagonal fields in the SL(N,R)/SO(N) scalar submanifolds of the full scalar sectors of the corresponding maximal supergravities, with N=8, 6 and 5. The embeddings were used for obtaining an interpretation of extremal D=4, 5 or 7 AdS domain walls in terms of distributed M-branes or D-branes in the higher dimensions. Although strong supporting evidence for the correctness of the embedding Ansatze was presented, a full proof of the consistency was not given. Here, we complete the proof, by showing explicitly that the full set of higher-dimensional equations of motion are satisfied if and only if the lower-dimensional fields satisfy the relevant scalar plus gravity equations.

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arXiv2000

Consistent SO(6) Reduction Of Type IIB Supergravity on S^5

Type IIB supergravity can be consistently truncated to the metric and the self-dual 5-form. We obtain the complete non-linear Kaluza-Klein S^5 reduction Ansatz for this theory, giving rise to gravity coupled to the fifteen Yang-Mills gauge fields of SO(6) and the twenty scalars of the coset SL(6,R)/SO(6). This provides a consistent embedding of this subsector of N=8, D=5 gauged supergravity in type IIB in D=10. We demonstrate that the self-duality of the 5-form plays a crucial role in the consistency of the reduction. We also discuss certain necessary conditions for a theory of gravity and an antisymmetric tensor in an arbitrary dimension D to admit a consistent sphere reduction, keeping all the massless fields. We find that it is only possible for D=11, with a 4-form field, and D=10, with a 5-form. Furthermore, in D=11 the full bosonic structure of eleven-dimensional supergravity is required, while in D=10 the 5-form must be self-dual. It is remarkable that just from the consistency requirement alone one would discover D=11 and type IIB supergravities, and that D=11 is an upper bound on the dimension.

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arXiv2000

Geometry of The Embedding of Supergravity Scalar Manifolds in D=11 and D=10

Several recent papers have made considerable progress in proving the existence of remarkable consistent Kaluza-Klein 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 S^7 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, for the purposes of lifting lower-dimensional solutions back to the higher dimension. The major complexity of the spherical reduction Ansatze comes from the spin-0 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 maximally-supersymmetric one. We briefly discuss the use of these emdedding Ansatze for the lifting of solutions back to the higher dimension.

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arXiv2000

Absorption by Extremal D3-branes

The absorption in the extremal D3-brane background is studied for a class of massless fields whose linear perturbations leave the ten-dimensional background metric unperturbed, as well as the minimally-coupled massive scalar. We find that various fields have the same absorption probability as that of the dilaton-axion system, which is given exactly via the Mathieu equation. We analyze the features of the absorption cross-sections in terms of effective Schrödinger potentials, conjecture a general form of the dual effective potentials, and provide explicit numerical results for the whole energy range. As expected, all partial-wave absorption probabilities tend to zero (one) at low (large) energies, and exhibit an oscillatory pattern as a function of energy. The equivalence of absorption probabilities for various modes has implications for the correlation functions on the field, including subleading contributions on the field-theory side. In particular, certain half-integer and integer spin fields have identical absorption probabilities, thus providing evidence that the corresponding operator pairs on the field theory side belong to the same supermultiplets.

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arXiv2000

Localised Gravity in the Singular Domain Wall Background?

We study singular, supersymmetric domain-wall solutions supported by the massive breathing mode scalars of, for example, sphere reductions in M-theory or string theory. The space-time on one side of such a wall is asymptotic to the Cauchy horizon of the anti-de Sitter (AdS) space-time. However, on the other side there is a naked singularity. The higher-dimensional embedding of these solutions has the novel interpretation of (sphere compactified) brane configurations in the domain ``inside the horizon region,'' with the singularity corresponding to the sphere shrinking to zero volume. The naked singularity is the source of an infinite attractive gravitational potential for the fluctuating modes. Nevertheless, the spectrum is bounded from below, continuous and positive definite, with the wave functions suppressed in the region close to the singularity. The massless bound state is formally excluded due to the boundary condition for the fluctuating mode wave functions at the naked singularity. However, a regularisation of the naked singularity, for example by effects of the order of the inverse string scale, in turn regularises the gravitational potential and allows for precisely one (massless) bound-state spin-2 fluctuating mode. We also contrast spectra in these domain wall backgrounds with those of the domain walls due to the massless modes of sphere reductions.

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arXiv2000

Domain Walls and Massive Gauged Supergravity Potentials

We point out that massive gauged supergravity potentials, for example those arising due to the massive breathing mode of sphere reductions in M-theory or string theory, allow for supersymmetric (static) domain wall solutions which are a hybrid of a Randall-Sundrum domain wall on one side, and a dilatonic domain wall with a run-away dilaton on the other side. On the anti-de Sitter (AdS) side, these walls have a repulsive gravity with an asymptotic region corresponding to the Cauchy horizon, while on the other side the runaway dilaton approaches the weak coupling regime and a non-singular attractive gravity, with the asymptotic region corresponding to the boundary of spacetime. We contrast these results with the situation for gauged supergravity potentials for massless scalar modes, whose supersymmetric AdS extrema are generically maxima, and there the asymptotic regime transverse to the wall corresponds to the boundary of the AdS spacetime. We also comment on the possibility that the massive breathing mode may, in the case of fundamental domain-wall sources, stabilize such walls via a Goldberger-Wise mechanism.

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arXiv1999

Symmetric Potentials of Gauged Supergravities in Diverse Dimensions and Coulomb Branch of Gauge Theories

A class of conformally flat and asymptotically anti-de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parameterise the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS_6 which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from massive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluctuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.

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arXiv1999

Four-dimensional N=4 SO(4) Gauged Supergravity from D=11

We construct the complete and explicit non-linear Kaluza-Klein Ansatz for deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional supergravity from the reduction of D=11 supergravity on S^7. This provides a way of interpreting all bosonic solutions of the four-dimensional gauged theory as exact solutions in eleven-dimensional supergravity. We discuss certain limiting forms of the Kaluza-Klein reduction, and compare them with related forms in the Freedman-Schwarz N=4 SU(2)xSU(2) gauged theory. This leads us to the result that the Freedman-Schwarz model is in fact a singular limiting case of the standard SO(4) gauged supergravity. We show that in this limit, our Ansatz for getting the SO(4) gauged theory as an S^7 reduction from D=11 indeed reduces to an S^3 x S^3 reduction from D=10, which makes contact with previous results in the literature. We also show that there is no distinction to be made between having equal or unequal values for the gauge coupling constants $g$ and $\tilde g$ of the two SU(2) gauge-group factors in the standard N=4 SO(4) gauged supergravity, whilst by contrast the ratio of $g$ to $\tilde g$ is a non-trivial parameter of the Freedman-Schwarz model.

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arXiv1999

Supercharges, Killing Spinors and Intersecting Gauge Five-branes

We obtain new solutions where a string and a pp-wave lie in the common worldvolume directions of the non-standard intersection of two gauge 5-branes in the heterotic string. The two 5-branes are supported by independent SU(2) Yang-Mills instantons in their respective (non-overlapping) transverse spaces. We present a detailed study of the unbroken supersymmetry, focusing especially on a comparison between a direct construction of Killing spinors and a counting of zero eigenvalues in the annticommutator of supercharges. The results are in agreement with some previous arguments, to the effect that additional zero eigenvalues resulting from a ``fine-tuning'' between positive-energy and negative-energy contributions from different components in an intersection are spurious, and should not be taken as an indication of supersymmetry enhancements. These observations have a general applicability that goes beyond the specific example we study in this paper.

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arXiv1999

Five-dimensional N=4, SU(2) X U(1) Gauged Supergravity from Type IIB

We construct the complete and explicit non-linear Kaluza-Klein ansatz for deriving the bosonic sector of N=4 SU(2)\times U(1) gauged five-dimensional supergravity from the reduction of type IIB supergravity on S^5. This provides the first complete example of such an S^5 reduction that includes non-abelian gauge fields, and it allows any bosonic solution of the five-dimensional N=4 gauged theory to be embedded in D=10.

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arXiv1999

Higher-dimensional Origin of D=3 Coset Symmetries

It is well known that the toroidal dimensional reduction of supergravities gives rise in three dimensions to theories whose bosonic sectors are described purely in terms of scalar degrees of freedom, which parameterise sigma-model coset spaces. For example, the reduction of eleven-dimensional supergravity gives rise to an E_8/SO(16) coset Lagrangian. In this paper, we dispense with the restrictions of supersymmetry, and study all the three-dimensional scalar sigma models G/H where G is a maximally-non-compact simple group, with H its maximal compact subgroup, and find the highest dimensions from which they can be obtained by Kaluza-Klein reduction. A magic triangle emerges with a duality between rank and dimension. Interesting also are the cases of Hermitean symmetric spaces and quaternionic spaces.

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arXiv1999

Exact Embedding of N=1, D=7 Gauged Supergravity in D=11

We obtain the explicit and complete bosonic non-linear Kaluza-Klein ansatz for the consistent S^4 reduction of D=11 supergravity to N=1, D=7 gauged supergravity. This provides a geometrical interpretation of the lower dimensional solutions from the eleven-dimensional point of view.

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arXiv1999

Gauged Six-dimensional Supergravity from Massive Type IIA

We obtain the complete non-linear Kaluza-Klein ansatz for the reduction of the bosonic sector of massive type IIA supergravity to the Romans F(4) gauged supergravity in six dimensions. The latter arises as a consistent warped S^4 reduction.

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arXiv1999

Superdualities, Brane Tensions and Massive IIA/IIB Duality

The gauge transformations of p-form fields in supergravity theories acquire a non-commuting character when one introduces potentials both for the theory's original field strengths and for their duals. This has previously been shown in the ``doubled'' formalism for maximal supergravities, where a generalised duality relation between original and dual field strengths replaces the equations of motion. In the doubled formalism, the gauge transformations generate a superalgebra, and the corresponding symmetries have accordingly been called ``superdualities.'' The corresponding Noether charges form a representation of the cohomology ring on the spacetime manifold. In this paper, we show that the gauge symmetry superalgebra implies certain non-trivial relations among the various p-brane tensions, which can straightforwardly be read off from the superalgebra commutation relations. This provides an elegant derivation of the brane-tension relations purely within a given theory, without the need to make use of duality relations between different theories, such as the type IIA/IIB T-duality, although the results are consistent with such dualities. We present the complete set of brane-tension relations in M-theory, in the type IIA and type IIB theories, and in all the lower-dimensional maximal supergravities. We also construct a doubled formalism for massive type IIA supergravity, and this enables us to obtain the brane-tension relations involving the D8-brane, purely within the framework of the massive IIA theory. We also obtain explicit transformations for the nine-dimensional T-duality between the massive type IIA theory and the Scherk-Schwarz reduced type IIB theory.

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arXiv1999

Domain-wall Supergravities from Sphere Reduction

Kaluza-Klein sphere reductions of supergravities that admit AdS x Sphere vacuum solutions are believed to be consistent. The examples include the S^4 and S^7 reductions of eleven-dimensional supergravity, and the S^5 reduction of ten-dimensional type IIB supergravity. In this paper we provide evidence that sphere reductions of supergravities that admit instead Domain-wall x Sphere vacuum solutions are also consistent, where the background can be viewed as the near-horizon structure of a dilatonic p-brane of the theory. The resulting lower-dimensional theory is a gauged supergravity that admits a domain wall, rather than AdS, as a vacuum solution. We illustrate this consistency by taking the singular limits of certain modulus parameters, for which the original S^n compactifying spheres (n=4,5 or 7) become S^p x R^q, with p=n-q<n. The consistency of the S^4, S^7 and S^5 reductions then implies the consistency of the S^p reductions of the lower-dimensional supergravities. In particular, we obtain explicit non-linear ansatze for the S^3 reduction of type IIA and heterotic supergravities, restricting to the U(1)^2 subgroup of the SO(4) gauge group of S^3. We also study the black hole solutions in the lower-dimensional gauged supergravities with domain-wall backgrounds. We find new domain-wall black holes which are not the singular-modulus limits of the AdS black holes of the original theories, and we obtain their Killing spinors.

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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

Instanton Moduli and Brane Creation

We obtain new intersecting 5-brane, string and pp-wave solutions in the heterotic string on a torus and on a K3 manifold. In the former case the 5-brane is supported by Yang-Mills instantons, and in the latter case both the 5-brane and the string are supported by the instantons. The instanton moduli are parameterised by the sizes and locations of the instantons. We exhibit two kinds of phase transition in which, for suitable choices of the instanton moduli, a 5-brane and/or a string can be created. One kind of phase transition occurs when the size of an instanton vanishes, while the other occurs when a pair of Yang-Mills instantons coalesce. We also study the associated five-dimensional black holes and the implications of these phase transitions for the black-hole entropy. Specifically, we find that the entropy of the three-charge black holes is zero when the instantons are separated and of non-zero scale size, but becomes non-zero (which can be counted miscrospically) after either of the phase transitions.

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