T.A. Tran

Embedding AdS black holes in ten and eleven dimensions

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

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.

Consistent SO(6) reduction of type IIB supergravity on S5

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.

Five-dimensional N=4, SU(2)×U(1) gauged supergravity from type IIB

Abstract We construct the complete and explicit non-linear Kaluza–Klein ansatz for deriving the bosonic sector of N =4 SU (2)× 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.

Euclidean-signature supergravities, dualities and instantons☆

Abstract 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 multicharge 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.

S3 and S4 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.

Classification of p-branes, NUTs, Waves and Intersections

We give a full classification of the multi-charge supersymmetric p-brane solutions in the massless and massive maximal supergravities in dimensions D ≥ 2 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.

Exact absorption probability in the extremal six-dimensional dyonic string background

We show that the minimally coupled massless scalar wave equation in the background of a six-dimensional extremal dyonic string (or D1{endash}D5-brane intersection) is exactly solvable, in terms of Mathieu functions. Using this fact, we calculate the absorption probabilities for these scalar waves and present 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 {open_quotes}noncritical{close_quotes} string). {copyright} {ital 1999} {ital The American Physical Society}

Closed-form Absorption Probability of Certain D = 5 and D = 4 Black Holes and Leading-Order Cross-Section of Generic Extremal p-branes

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.

U DUALITY AS GENERAL COORDINATE TRANSFORMATIONS, AND SPACE–TIME GEOMETRY

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 discretized 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 Tn can be related by duality to a compactification on a small torus, if and only if n≥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≥3.