Pure de Sitter Supergravity

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.Comment: 22 pages, version to appear in PRD; v4: minor typos corrected; v5: correction of torsion lagrangian (2.2); v6: Minor error in Sec.4.3 corrected. This simplifies previous proof that any zero mode vanishes identicall

Anomaly Cancellation in Supergravity with Fayet-Iliopoulos Couplings

We review and clarify the cancellation conditions for gauge anomalies which occur when N=1, D=4 supergravity is coupled to a Kahler non-linear sigma-model with gauged isometries and Fayet-Iliopoulos couplings. For a flat sigma-model target space and vanishing Fayet-Iliopoulos couplings, consistency requires just the conventional anomaly cancellation conditions. A consistent model with non-vanishing Fayet-Iliopoulos couplings is unlikely unless the Green-Schwarz mechanism is used. In this case the U(1) gauge boson becomes massive and the D-term potential receives corrections. A Green-Schwarz mechanism can remove both the abelian and certain non-abelian anomalies in models with a gauge non-invariant Kahler potential.Comment: 27 page

Elastic effects of vacancies in strontium titanate: Short- and long-range strain fields, elastic dipole tensors, and chemical strain

We present a study of the local strain effects associated with vacancy defects in strontium titanate and report the first calculations of elastic dipole tensors and chemical strains for point defects in perovskites. The combination of local and long-range results will enable determination of x-ray scattering signatures that can be compared with experiments. We find that the oxygen vacancy possesses a special property -- a highly anisotropic elastic dipole tensor which almost vanishes upon averaging over all possible defect orientations. Moreover, through direct comparison with experimental measurements of chemical strain, we place constraints on the possible defects present in oxygen-poor strontium titanate and introduce a conjecture regarding the nature of the predominant defect in strontium-poor stoichiometries in samples grown via pulsed laser deposition. Finally, during the review process, we learned of recent experimental data, from strontium titanate films deposited via molecular-beam epitaxy, that show good agreement with our calculated value of the chemical strain associated with strontium vacancies.Comment: 14 pages, 11 figures, 4 table

From Fake Supergravity to Superstars

The fake supergravity method is applied to 5-dimensional asymptotically AdS spacetimes containing gravity coupled to a real scalar and an abelian gauge field. The motivation is to obtain bulk solutions with R x S^3 symmetry in order to explore the AdS/CFT correspondence when the boundary gauge theory is on R x S^3. A fake supergravity action, invariant under local supersymmetry through linear order in fermion fields, is obtained. The gauge field makes things more restrictive than in previous applications of fake supergravity which allowed quite general scalar potentials. Here the superpotential must take the form W(\phi) ~ exp(-k\phi) + c exp(2\phi/(3k)), and the only freedom is the choice of the constant k. The fermion transformation rules of fake supergravity lead to fake Killing spinor equations. From their integrability conditions, we obtain first order differential equations which we solve analytically to find singular electrically charged solutions of the Lagrangian field equations. A Schwarzschild mass term can be added to produce a horizon which shields the singularity. The solutions, which include "superstars", turn out to be known in the literature. We compute their holographic parameters.Comment: 42 pages, 3 figure

Star product and the general Leigh-Strassler deformation

We extend the definition of the star product introduced by Lunin and Maldacena to study marginal deformations of N=4 SYM. The essential difference from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with charges in a corresponding diagonal matrix, we consider two Z_3-symmetries followed by an SU(3) transformation, with resulting off-diagonal elements. From this procedure we obtain a more general Leigh-Strassler deformation, including cubic terms with the same index, for specific values of the coupling constants. We argue that the conformal property of N=4 SYM is preserved, in both beta- (one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the deformation for each amplitude can be extracted in a prefactor. We also conclude that the obtained amplitudes should follow the iterative structure of MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A added, v4: clarification in section 3.

Holography and Defect Conformal Field Theories

We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x S^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3 defect. We propose a complete Lagrangian for the field theory dual, a novel "defect superconformal field theory" wherein a subset of the fields of N=4 SYM interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4), and we construct the map to a set of dual gauge-invariant defect operators O_3 possessing integer conformal dimensions. Gravity calculations of and are given. Spacetime and N-dependence matches expectations from dCFT, while the behavior as functions of lambda = g^2 N at strong and weak coupling is generically different. We comment on a class of correlators for which a non-renormalization theorem may still exist. Partial evidence for the conformality of the quantum theory is given, including a complete argument for the special case of a U(1) gauge group. Some weak coupling arguments which illuminate the duality are presented.Comment: 47 pages, LaTeX, 2 figures, feynmf. v2: fixed minor errors, added references. v3: fixed more typo