arXiv subjects
Publications and source records attributed to H. Lu.
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.
We obtain the closed-form absorption probabilities for minimally-coupled massless scalars propagating in the background of D=5 single-charge and D=4 two-charge black holes. These are the only two examples of extremal black holes with non-vanishing absorption probabilities that can be solved in closed form for arbitrary incident frequencies. In both cases, the absorption probability vanishes when the frequency is below a certain threshold, and we discuss the connection between this phenomenon and the behaviour of geodesics in these black hole backgrounds. We also obtain leading-order absorption cross-sections for generic extremal p-branes, and show that the expression for the cross-section as a function of frequency coincides with the leading-order dependence of the entropy on the temperature in the corresponding near-extremal p-branes.
We show that the minimally coupled massless scalar wave equation in the background of an six-dimensional extremal dyonic string (or D1-D5 brane intersection) is exactly solvable, in terms of Mathieu functions. Using this fact, we calculate absorption probabilities for these scalar waves, and present the explicit results for the first few low energy corrections to the leading-order expressions. For a specific tuning of the dyonic charges one can reach a domain where the low energy absorption probability goes to zero with inverse powers of the logarithm of the energy. This is a dividing domain between the regime where the low energy absorption probability approaches zero with positive powers of energy and the regime where the probability is an oscillatory function of the logarithm of the energy. By the conjectured AdS/CFT correspondence, these results shed novel light on the strongly coupled two-dimensional field theory away from its infrared conformally invariant fixed point (the strongly coupled ``non-critical'' string).
We study the space-times of non-extremal intersecting p-brane configurations in M-theory, where one of the components in the intersection is a ``NUT,'' i.e. a configuration of the Taub-NUT type. Such a Taub-NUT configuration corresponds, upon compactification to D=4, to a Gross-Perry-Sorkin (GPS) monopole. We show that in the decoupling limit of the CFT/AdS correspondence, the 4-dimensional transverse space of the NUT configuration in D=5 is foliated by surfaces that are cyclic lens spaces S^3/Z_N, where N is the quantised monopole charge. By contrast, in D=4 the 3-dimensional transverse space of the GPS monopole is foliated by 2-spheres. This observation provides a straightforward interpretation of the microscopics of a D=4 string-theory black hole, with a GPS monopole as one of its constituents, in terms of the corresponding D=5 black hole with no monopole. Using the fact that the near-horizon region of the NUT solution is a lens space, we show that if the effect of the Kaluza-Klein massive modes is neglected, p-brane configurations can be obtained from flat space-time by means of a sequence of dimensional reductions and oxidations, and U-duality transformations.
We study the duality relationship between M-theory and heterotic string theory at the classical level, emphasising the transformations between the Kaluza-Klein reductions of these two theories on the K3 and T^3 manifolds. Particular attention is devoted to the corresponding structures of sigma-model cosets and the correspondence between the p-brane charge lattices. We also present simple and detailed derivations of the global symmetries and coset structures of the toroidally-compactified heterotic theory in all dimensions D \ge 3, making use of the formalism of solvable Lie algebras.
We study the spacetimes of the near-horizon regions in D3-brane, M2-brane and M5-brane configurations, in cases where there is a pp-wave propagating along a direction in the world-volume. While non-extremal configurations of this kind locally have the same Carter-Novotny-Horsky-type metrics as those without the wave, taking the BPS limit results instead in Kaigorodov-type metrics, which are homogeneous, but preserve 1/4 of the supersymmetry, and have global and local structures that are quite different from the corresponding anti-de Sitter spacetimes associated with solutions where there is no pp-wave. We show that the momentum density of the system is non-vanishing and held fixed under the gravity decoupling limit. In view of the AdS/CFT correspondence, M-theory and type IIB theory in the near-horizon region of these boosted BPS-configurations specifies the corresponding CFT on the boundary in an infinitely-boosted frame with constant momentum density. We model the microstates of such boosted configurations (which account for the microscopic counting of near-extremal black holes in D=7, D=9 and D=6) by those of a boosted dilute massless gas in a d=4, d=3 and d=6 spacetime respectively. Thus we obtain a simple description for the entropy of 2-charge black holes in D=7,9 and 6 dimensions. The paper includes constructions of generalisations of the Kaigorodov and Carter-Novotny-Horsky metrics in arbitrary spacetime dimensions, and an investigation of their properties.
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.
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.
We analyse the global (rigid) symmetries that are realised on the bosonic fields of the various supergravity actions obtained from eleven-dimensional supergravity by toroidal compactification followed by the dualisation of some subset of fields. In particular, we show how the global symmetries of the action can be affected by the choice of this subset. This phenomenon occurs even with the global symmetries of the equations of motion. A striking regularity is exhibited by the series of theories obtained respectively without any dualisation, with the dualisation of only the Ramond-Ramond fields of the type IIA theory, with full dualisation to lowest degree forms, and finally for certain inverse dualisations (increasing the degrees of some forms) to give the type IIB series. These theories may be called the GL_A, D, E and GL_B series respectively. It turns out that the scalar Lagrangians of the E series are sigma models on the symmetric spaces K(E_{11-D})\backslash E_{11-D} (where K(G) is the maximal compact subgroup of G) and the other three series lead to models on homogeneous spaces K(G) \backslash G\semi \R^s. These can be understood from the E series in terms of the deletion of positive roots associated with the dualised scalars, which implies a group contraction. We also propose a constrained Lagrangian version of the even dimensional theories exhibiting the full duality symmetry and begin a systematic analysis of abelian duality subalgebras.
We introduce a doubled formalism for the bosonic sector of the maximal supergravities, in which a Hodge dual potential is introduced for each bosonic field (except for the metric). The equations of motion can then be formulated as a twisted self-duality condition on the total field strength \G, which takes its values in a Lie superalgebra. This doubling is invariant under dualisations; it allows a unification of the gauge symmetries of all degrees, including the usual U-dualities that have degree zero. These ``superdualities'' encompass the dualities for all choices of polarisation (i.e. the choices between fields and their duals). All gauge symmetries appear as subgroups of finite-dimensional supergroups, with Grassmann coefficients in the differential algebra of the spacetime manifold.
We show that the full global symmetry groups of all the D-dimensional maximal supergravities can be described in terms of the closure of the internal general coordinate transformations of the toroidal compactifications of D=11 supergravity and of type IIB supergravity, with type IIA/IIB T-duality providing an intertwining between the two pictures. At the quantum level, the part of the U-duality group that corresponds to the surviving discretised internal general coordinate transformations in a given picture leaves the internal torus invariant, while the part that is not described by internal general coordinate transformations can have the effect of altering the size or shape of the internal torus. For example, M-theory compactified on a large torus T^n can be related by duality to a compactification on a small torus, if and only if n\ge 3. We also discuss related issues in the toroidal compactification of the self-dual string to D=4. An appendix includes the complete results for the toroidal reduction of the bosonic sector of type IIB supergravity to arbitrary dimensions D\ge3.
We derive simple general expressions for the explicit Killing spinors on the n-sphere, for arbitrary n. Using these results we also construct the Killing spinors on various AdS x Sphere supergravity backgrounds, including AdS_5 x S^5$, AdS_4 x S^7 and AdS_7 x S^4. In addition, we extend previous results to obtain the Killing spinors on the hyperbolic spaces H^n.
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.
We study the Euclidean-signature supergravities that arise by compactifying D=11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D=8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multi-charge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D-3)-brane solutions.
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.
We give a full classification of the multi-charge supersymmetric $p$-brane solutions in the massless and massive maximal supergravities in dimensions $D\ge2$ obtained from the toroidal reduction of eleven-dimensional supergravity. We derive simple universal rules for determining the fractions of supersymmetry that they preserve. By reversing the steps of dimensional reduction, the $p$-brane solutions become intersections of $p$-branes, NUTs and waves in D=10 or D=11. Having classified the lower-dimensional $p$-branes, this provides a classification of all the intersections in D=10 and D=11 where the harmonic functions depend on the space transverse to all the individual objects. We also discuss the structure of U-duality multiplets of $p$-brane solutions, and show how these translate into multiplets of harmonic and non-harmonic intersections.
We present the form of the Dirac quantisation condition for the p-form charges carried by p-brane solutions of supergravity theories. This condition agrees precisely with the conditions obtained in lower dimensions, as is necessary for consistency with Kaluza-klein dimensional reduction. These considerations also determine the charge lattice of BPS soliton states, which proves to be a universal modulus-independent lattice when the charges are defined to be the canonical charges corresponding to the quantum supergravity symmetry groups.
We study some geometrical and topological aspects of the generalised dimensional reduction of supergravities in D=11 and D=10 dimensions, which give rise to massive theories in lower dimensions. In these reductions, a global symmetry is used in order to allow some of the fields to have a non-trivial dependence on the compactifying coordinates. Global consistency in the internal space imposes topological restrictions on the parameters of the compactification as well as the structure of the space itself. Examples that we consider include the generalised reduction of the type IIA and type IIB theories on a circle, and also the massive ten-dimensional theory obtained by the generalised reduction of D=11 supergravity.