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 transverse 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. IntroductionAnti-de Sitter black hole solutions of gauged extended supergravities [1] are currently attracting a good deal of attention [2,3,4,5,6,7,8,9,10,11,12] due, in large part, to the correspondence between anti-de Sitter space and conformal field theories on its boundary [13,14,15,16]. These gauged extended supergravities can arise as the massless modes of various Kaluza-Klein compactifications of both D = 11 and D = 10 supergravities. The three examples studied in the paper will be gauged D = 4, N = 8 SO(8) supergravity [17, 18] arising from D = 11 supergravity on S 7 [19, 20] whose black hole solutions are discussed in [7]; gauged D = 5, N = 8 SO(6) supergravity [21, 22] arising from Type IIB supergravity on S 5 [23, 24, 25] whose black hole solutions are discussed in [2, 6]; and gauged D = 7, N = 4 SO(5) supergravity [21, 26] arising from D = 11 supergravity on S 4 [27]whose black hole solutions are given in section 4.2 and in [9,28]. 1 In the absence of the black holes, these three AdS compactifications are singled out as arising from the near-horizon geometry of the extremal non-rotating M2, D3 and M5 branes [29,30,31,32]. One of our goals will be to embed these known lower-dimensional black hole solutions into ten or eleven dimensions, thus allowing a higher dimensional interpretation in terms of rotating M2, D3 and M5-branes.Since these gauged supergravity theories may be obtained by consistently truncating the massive modes of the full Kaluza-Klein theories, it follows that all solutions of the lower-dimensional theories will also be solutions of the higher-dimensional ones [33,34]. In principle, therefore, once we know the Kaluza-Klein ansatz for the massless sector, it ought to be straightforward to read off the higher dimensional solutions. It practice, however, this is a formidable task. The correct massless ansatz for the S 7 compactification took many years to finalize [35,36], and is still highly implicit, while for the S 5 and S 4 compactifications, the complete massless ansätze are still unknown. For our present purposes, it suffices to consider truncations of the gauged supergravities to include only gauge fields in the Cartan subalgebras ...

We provide a pedagogical introduction to a recently studied class of phenomenologically interesting string models, known as Intersecting D-Brane Models. The gauge fields of the Standard-Model are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersections can give rise to chiral fermions. We address the basic issues and also provide an overview of the recent activity in this field. This article is intended to serve non-experts with explanations of the fundamental aspects, and also to provide some orientation for both experts and nonexperts in this active field of string phenomenology. † Permanent address

In a theory where the cosmological constant Λ or the gauge coupling constant g arises as the vacuum expectation value, its variation should be included in the first law of thermodynamics for black holes. This becomes dE = T dSwhere E is now the enthalpy of the spacetime, and Θ, the thermodynamic conjugate of Λ, is proportional to an effective volume V = − 16πΘ D−2 "inside the event horizon." Here we calculate Θ and V for a wide variety of D-dimensional charged rotating asymptotically AdS black hole spacetimes, using the first law or the Smarr relation. We compare our expressions with those obtained by implementing a suggestion of Kastor, Ray and Traschen, involving Komar integrals and Killing potentials, which we construct from 1 conformal Killing-Yano tensors. We conjecture that the volume V and the horizon areaA D−2 is the volume of the unit (D − 2)-sphere, and we show that this is obeyed for a wide variety of black holes, and saturated for Schwarzschild-AdS. Intriguingly, this inequality is the "inverse" of the isoperimetric inequality for a volume V in Euclidean (D−1) space bounded by a surface of area A, for which R ≤ 1. Our conjectured Reverse Isoperimetric Inequality can be interpreted as the statement that the entropy inside a horizon of a given "volume" V is maximised for Schwarzschild-AdS. The thermodynamic definition of V requires a cosmological constant (or gauge coupling constant).However, except in 7 dimensions, a smooth limit exists where Λ or g goes to zero, providing a definition of V even for asymptotically-flat black holes.2

We systematically investigate instanton corrections from wrapped Euclidean D-branes to the matter field superpotential of various classes of N=1 supersymmetric D-brane models in four dimensions. Both gauge invariance and the counting of fermionic zero modes provide strong constraints on the allowed non-perturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a oneloop vacuum diagram. For concreteness we focus on E2-instanton effects in Type IIA vacua with intersecting D6-branes, however the same structure emerges for Type IIB and heterotic vacua. The instantons wrapping rigid cycles can potentially destabilise the vacuum or generate perturbatively absent matter couplings such as proton decay operators, µ-parameter or right-handed neutrino Majorana mass terms. The latter allow the realization of the seesaw mechanism for MSSM like intersecting D-brane models.

We construct N = 1 supersymmetric four-dimensional orientifolds of type IIA on T 6 /(Z 2 × Z 2 ) with D6-branes intersecting at angles. The use of D6branes not fully aligned with the O6-planes in the model allows for a construction of many supersymmetric models with chiral matter, including those with the Standard Model and grand unified gauge groups. We perform a search for realistic gauge sectors, and construct the first example of a supersymmetric type II orientifold with SU (3) C × SU (2) L × U (1) Y gauge group and three quark-lepton families. In addition to the supersymmetric Standard Model content, the model contains right-handed neutrinos, a (chiral but anomalyfree) set of exotic multiplets, and diverse vector-like multiplets. The general class of these constructions are related to familiar type II orientifolds by small instanton transitions, which in some cases change the number of generations, as discussed in specific models. These constructions are supersymmetric only for special choices of untwisted moduli. We briefly discuss the supersymmetry breaking effects away from that point. The M-theory lift of this general class of supersymmetric orientifold models should correspond to purely geometrical backgrounds admitting a singular G 2 holonomy metric and leading to four-dimensional M-theory vacua with chiral fermions.

Seven-manifolds of G 2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six-manifolds. We find first-order equations for a new family of G 2 metrics D 7 , with S 3 × S 3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B 7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D 7 metrics' non-trivial parameter characterises the squashing of an S 3 bolt, which limits to S 2 at weak coupling. In general the D 7 metrics are asymptotically locally conical, with a nowhere-singular circle action.

We study the thermodynamic stability of charged black holes in gauged supergravity theories in D = 5, D = 4 and D = 7. We find explicitly the location of the Hawking-Page phase transition between charged black holes and the pure anti-de Sitter space-time, both in the grand-canonical ensemble, where electric potentials are held fixed, and in the canonical ensemble, where total charges are held fixed. We also find the explicit local thermodynamic stability constraints for black holes with one non-zero charge. In the grandcanonical ensemble, there is in general a region of phase space where neither the anti-de Sitter space-time is dynamically preferred, nor are the charged black holes thermodynamically stable. But in the canonical ensemble, anti-de Sitter space-time is always dynamically preferred in the domain where black holes are unstable.We demonstrate the equivalence of large R-charged black holes in D = 5, D = 4 and D = 7 with spinning near-extreme D3-, M2-and M5-branes, respectively. The mass, the charges and the entropy of such black holes can be mapped into the energy above extremality, the angular momenta and the entropy of the corresponding branes. We also note a peculiar numerological sense in which the grand-canonical stability constraints for large charge black holes in D = 4 and D = 7 are dual, and in which the D = 5 constraints are self-dual.

We construct the first three family N 1 supersymmetric string model with standard model gauge group SU͑3͒ C 3 SU͑2͒ L 3 U͑1͒ Y from an orientifold of type IIA theory on T 6 ͑͞Z 2 3 Z 2 ͒ and D6-branes intersecting at angles. In addition to the minimal supersymmetric standard model particles, the model contains right-handed neutrinos, a chiral (but anomaly-free) set of exotic multiplets, and extra vectorlike multiplets. We discuss some phenomenological features of this model. DOI: 10.1103/PhysRevLett.87.201801 PACS numbers: 11.10.Kk, 11.25.Mj, 12.60.Jv, 98.80.Cq The space of classical string vacua is highly degenerate, and at present we are unable to make definitive statements about how the string vacuum describing our universe is selected. Nonetheless, one can use phenomenological constraints as guidelines to construct semirealistic string models and explore, with judicious assumptions, the resulting phenomenology. The purpose of such explorations is, of course, not to find the model which would fully describe our world, but to examine the generic features of these string derived solutions.Until a few years ago, such explorations were carried out mainly in the framework of weakly coupled heterotic string theory. Indeed, a number of semirealistic string models have been constructed and analyzed [1]. However, an important lesson from string duality is that these models represent only a corner of M theory -the string vacuum describing our world may well be in a completely different regime in which the perturbative description of heterotic string theory breaks down [2]. Fortunately, the advent of D-branes allows for the construction of semirealistic string models in another calculable regime, as illustrated by the various four-dimensional N 1 supersymmetric type II orientifolds ([3-12] and references therein) constructed using conformal field theory techniques. However, the constraints on supersymmetric fourdimensional models are rather restrictive, leading to not fully realistic gauge sectors and matter contents. Motivated by the search for standard model-like solutions, several discrete or continuous deformations of this class of models have been explored. They include the following: (i) blowing-up of orientifold singularities [13,14], (ii) locating the branes at different points in the internal space (see, e.g., [9,12,15]) which in a T -dual picture corresponds to turning on continuous or discrete Wilson lines, (iii) introduction of discrete values for the Neveu-Schwarz -Neveu-Schwarz (NS-NS) B field [7,16] which in the T-dual picture corresponds to tilting the compactification tori, (iv) introduction of gauge fluxes in the D-brane world volumes (see [17] for an earlier discussion, and [18,19] for supersymmetric D 6 models), which in the T -dual version corresponds to D-branes intersecting at angles (hence closely related to models in [20,21]).An appealing feature of (iv) is that generically, there exists chiral fermions where D-branes intersect [22]. Their multiplicity is hence determined by a topological q...