On Dimensional Reduction of Magical Supergravity Theories

We prove, by a direct dimensional reduction and an explicit construction of the group manifold, that the nonlinear sigma model of the dimensionally reduced three-dimensional A = R magical supergravity is F4(+4)/(USp(6)xSU(2)). This serves as a basis for the solution generating technique in this supergravity as well as allows to give the Lie algebraic characterizations to some of the parameters and functions in the original D = 5 Lagrangian. Generalizations to other magical supergravities are also discussed.Comment: 15 page

Lama Fermentasi terhadap Mutu Teh Daun Sirsak (Annona Muricata L.)

The purposes of this study was to obtain the effect of fermentation on the quality of soursop leaf tea by fermentation. Soursop leaf tea processing using the method of processing black tea. The method used in this study was completely randomized design with 4 treatments and 4 replications. The treatment used were F1(1 hour fermentation), F2 (2 hours fermentation), F3 (3 hours fermentation), F4 (4 hours fermentation). The results showed that the long of fermentation of tea leaves of the soursop significant effect on water content, levels of tannins, antioxidant activity, assessment of sensory descriptive and hedonic well as colour, aroma, taste and acceptance as a whole tea leaves of the soursop, but did not significantly affect the ash content. The best treatment was F4 (4 hours fermentation) based on water content of 1.31%, ash content of 5.82%, tannin content of 0.51%, the antioxidant levels of 28.733 ppm, descriptive sensory assessment and hedonic soursop leaf tea which has a brown colour and preferred by the panelist's. Soursop leaf tea flavor is slightly tart and flavorful leaves of the soursop so preferred by the panelist's. While the overall assessment of soursop leaf tea is also preferred by the panelist's

A magic pyramid of supergravities

By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently tied in with the more familiar R,C,H,O description of spacetime to give a unified division-algebraic description of extended super Yang-Mills in D = 3, 4, 6, 10. Here, these constructions are brought together resulting in a magic pyramid of supergravities. The base of the pyramid in D = 3 is the known 4x4 magic square, while the higher levels are comprised of a 3x3 square in D = 4, a 2x2 square in D = 6 and Type II supergravity at the apex in D = 10. The corresponding U-duality groups are given by a new algebraic structure, the magic pyramid formula, which may be regarded as being defined over three division algebras, one for spacetime and each of the left/right Yang-Mills multiplets. We also construct a conformal magic pyramid by tensoring conformal supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of an exotic theory with G/H duality structure F4(4)/Sp(3) x Sp(1).Comment: 30 pages, 6 figures. Updated to match published version. References and comments adde

Towards 4-point correlation functions of any 1/2-BPS operators from supergravity

The quartic effective action for Kaluza-Klein modes that arises upon compactification of type IIB supergravity on the five-sphere S^5 is a starting point for computing the four-point correlation functions of arbitrary weight 1/2-BPS operators in N=4 super Yang-Mills theory in the supergravity approximation. The apparent structure of this action is rather involved, in particular it contains quartic terms with four derivatives which cannot be removed by field redefinitions. By exhibiting intricate identities between certain integrals involving spherical harmonics of S^5 we show that the net contribution of these four-derivative terms to the effective action vanishes. Our result is in agreement with and provides further support to the recent conjecture on the Mellin space representation of the four-point correlation function of any 1/2-BPS operators in the supergravity approximation.Comment: 12 page

Weyl Groups in AdS(3)/CFT(2)

The system of D1 and D5 branes with a Kaluza-Klein momentum is re-investigated using the five-dimensional U-duality group E_{6(+6)}(Z). We show that the residual U-duality symmetry that keeps this D1-D5-KK system intact is generically given by a lift of the Weyl group of F_{4(+4)}, embedded as a finite subgroup in E_{6(+6)}(Z). We also show that the residual U-duality group is enhanced to F_{4(+4)}(Z) when all the three charges coincide. We then apply the analysis to the AdS(3)/CFT(2) correspondence, and discuss that among 28 marginal operators of CFT(2) which couple to massless scalars of AdS(3) gravity at boundary, 16 would behave as exactly marginal operators for generic D1-D5-KK systems. This is shown by analyzing possible three-point couplings among 42 Kaluza-Klein scalars with the use of their transformation properties under the residual U-duality group.Comment: 20 pages, 3 figue

Squaring the Magic

We construct and classify all possible Magic Squares (MS's) related to Euclidean or Lorentzian rank-3 simple Jordan algebras, both on normed division algebras and split composition algebras. Besides the known Freudenthal-Rozenfeld-Tits MS, the single-split G\"unaydin-Sierra-Townsend MS, and the double-split Barton-Sudbery MS, we obtain other 7 Euclidean and 10 Lorentzian novel MS's. We elucidate the role and the meaning of the various non-compact real forms of Lie algebras, entering the MS's as symmetries of theories of Einstein-Maxwell gravity coupled to non-linear sigma models of scalar fields, possibly endowed with local supersymmetry, in D = 3, 4 and 5 space-time dimensions. In particular, such symmetries can be recognized as the U-dualities or the stabilizers of scalar manifolds within space-time with standard Lorentzian signature or with other, more exotic signatures, also relevant to suitable compactifications of the so-called M*- and M'- theories. Symmetries pertaining to some attractor U-orbits of magic supergravities in Lorentzian space-time also arise in this framework.Comment: 21 pages, 1 figure, 20 tables; reference adde

Black hole solutions to the F4F_4-model and their orbits (I)

In this paper we continue the program of the classification of nilpotent orbits using the approach developed in arXiv:1107.5986, within the study of black hole solutions in D=4 supergravities. Our goal in this work is to classify static, single center black hole solutions to a specific N=2 four dimensional "magic" model, with special K\"ahler scalar manifold ${\rm Sp}(6,\mathbb{R})/{\rm U}(3)$, as orbits of geodesics on the pseudo-quaternionic manifold ${\rm F}_{4(4)}/[{\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})]$ with respect to the action of the isometry group ${\rm F}_{4(4)}$. Our analysis amounts to the classification of the orbits of the geodesic "velocity" vector with respect to the isotropy group $H^*={\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})$, which include a thorough classification of the \emph{nilpotent orbits} associated with extremal solutions and reveals a richer structure than the one predicted by the $\beta-\gamma$ labels alone, based on the Kostant Sekiguchi approach. We provide a general proof of the conjecture made in arXiv:0908.1742 which states that regular single center solutions belong to orbits with coinciding $\beta-\gamma$ labels. We also prove that the reverse is not true by finding distinct orbits with the same $\beta-\gamma$ labels, which are distinguished by suitably devised tensor classifiers. Only one of these is generated by regular solutions. Since regular static solutions only occur with nilpotent degree not exceeding 3, we only discuss representatives of these orbits in terms of black hole solutions. We prove that these representatives can be found in the form of a purely dilatonic four-charge solution (the generating solution in D=3) and this allows us to identify the orbit corresponding to the regular four-dimensional metrics.Comment: 81 pages, 24 tables, new section 4.4 about the fake superpotential added, typos corrected, references added, accepted in Nuclear Physics B.

Cosmic Billiards with Painted Walls in Non-Maximal Supergravities: a worked out example

The derivation of smooth cosmic billiard solutions through the compensator method is extended to non maximal supergravities. A new key feature is the non-maximal split nature of the scalar coset manifold. To deal with this, one needs the theory of Tits Satake projections leading to maximal split projected algebras. Interesting exact solutions that display several smooth bounces can thus be derived. From the analysis of the Tits Satake projection emerges a regular scheme for all non maximal supergravities and a challenging so far unobserved structure, that of the paint group G-paint. This latter is preserved through dimensional reduction and provides a powerful tool to codify solutions. It appears that the dynamical walls on which the cosmic ball bounces come actually in painted copies rotated into each other by G-paint. The effective cosmic dynamics is that dictated by the maximal split Tits Satake manifold plus paint. We work out in details the example provided by N=6,D=4 supergravity, whose scalar manifold is the special Kahlerian SO*(12)}/SU(6)xU(1). In D=3 it maps to the quaternionic E_7(-5)/ SO(12) x SO(3). From this example we extract a scheme that holds for all supergravities with homogeneous scalar manifolds and that we plan to generalize to generic special geometries. We also comment on the merging of the Tits-Satake projection with the affine Kac--Moody extensions originating in dimensional reduction to D=2 and D=1.Comment: 52 pages, 4 figures, 9 tables, paper. Few misprints correcte