On the Embedding of Space-Time Symmetries into Simple Superalgebras

We explore the embedding of Spin groups of arbitrary dimension and signature into simple superalgebras in the case of extended supersymmetry. The R-symmetry, which generically is not compact, can be chosen compact for all the cases that are congruent mod 8 to the physical conformal algebra so($D-2$,2), $D\geq 3$. An $\rm{so}(1,1)$ grading of the superalgebra is found in all cases. Central extensions of super translation algebras are studied in this framework.Comment: AMS LaTeX, 16 page

11-Dimensional Supergravity Compactified on Calabi-Yau Threefolds

We consider generic features of eleven dimensional supergravity compactified down to five dimensions on an arbitrary Calabi-Yau threefold.Comment: TeX, harvmac, 8 pg

Low-Temperature Quantum Critical Behaviour of Systems with Transverse Ising-like Intrinsic Dynamics

The low-temperature properties and crossover phenomena of $d$-dimensional transverse Ising-like systems within the influence domain of the quantum critical point are investigated solving the appropriate one-loop renormalization group equations. The phase diagram is obtained near and at $d=3$ and several sets of critical exponents are determined which describe different responses of a system to quantum fluctuations according to the way of approaching the quantum critical point. The results are in remarkable agreement with experiments for a wide variety of compounds exhibiting a quantum phase transition, as the ferroelectric oxides and other displacive systems.Comment: 36 pages, 2 figures, accepted in Physica

Supergravity Predictions on Conformal Field Theories

We give an update on recent results about the matching between CFT operators and KK states in the AdS/CFT correspondence, and add some new comments on the realization of the baryonic symmetries from the supergravity point of view.Comment: 8 pages, uses JHEP.cls, Contribution to the proceedings of the TMR Conference on Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Paris, 1-7 September 199

M Theory on the Stiefel manifold and 3d Conformal Field Theories

We compute the mass and multiplet spectrum of M theory compactified on the product of AdS(4) spacetime by the Stiefel manifold V(5,2)=SO(5)/SO(3), and we use this information to deduce via the AdS/CFT map the primary operator content of the boundary N=2 conformal field theory. We make an attempt for a candidate supersymmetric gauge theory that, at strong coupling, should be related to parallel M2-branes on the singular point of the non-compact Calabi-Yau four-fold $\sum_{a=1}^5 z_a^2 = 0$, describing the cone on V(5,2).Comment: Latex, 28 page

On the Super Higgs Effect in Extended Supergravity

We consider the reduction of supersymmetry in N-extended four dimensional supergravity via the super Higgs mechanism in theories without cosmological constant. We provide an analysis largely based on the properties of long and short multiplets of Poincare' supersymmetry. Examples of the super Higgs phenomenon are realized in spontaneously broken N=8 supergravity through the Scherk-Schwarz mechanism and in superstring compactification in presence of brane fluxes. In many models the massive vectors count the difference in number of the translation isometries of the scalar sigma-model geometries in the broken and unbroken phase.Comment: Version to appear on Nuclear Physics

Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds

We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.Comment: 31 pp. no figures, latex, some modifications at pag 21, a missing term in 4.51 corrected. Discussion on BRST symmetry improve

Curvatures and potential of M-theory in D=4 with fluxes and twist

We give the curvatures of the free differential algebra (FDA) of M--theory compactified to D=4 on a twisted seven--torus with the 4--form flux switched on. Two formulations are given, depending on whether the 1--form field strengths of the scalar fields (originating from the 3--form gauge field $\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonic equations of motion and discuss at length the scalar potential which emerges in this type of compactifications. For flat groups we show the equivalence of this potential with a dual formulation of the theory which has the full \rE_{7(7)} symmetry.Comment: 14 pages, LaTeX source, typos correcte

Picard-Fuchs Equations and Special Geometry

We investigate the system of holomorphic differential identities implied by special K\"ahlerian geometry of four-dimensional N=2 supergravity. For superstring compactifications on \cy threefolds these identities are equivalent to the Picard-Fuchs equations of algebraic geometry that are obeyed by the periods of the holomorphic three-form. For one variable they reduce to linear fourth-order equations which are characterized by classical $W$-generators; we find that the instanton corrections to the Yukawa couplings are directly related to the non-vanishing of $w_4$. We also show that the symplectic structure of special geometry can be related to the fact that the Yukawa couplings can be written as triple derivatives of some holomorphic function $F$. Moreover, we give the precise relationship of the Yukawa couplings of special geometry with three-point functions in topological field theory.Comment: 43 page

Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes

We present the supersymmetric completion of the M-theory free differential algebra resulting from a compactification to four dimensions on a twisted seven-torus with 4-form and 7-form fluxes turned on. The super--curvatures are given and the local supersymmetry transformations derived. Dual formulations of the theory are discussed in connection with classes of gaugings corresponding to diverse choices of vacua. This also includes seven dimensional compactifications on more general spaces not described by group manifolds.Comment: 19 pages, LaTeX, typos corrected, references adde