Deformations of generalized calibrations and compact non-Kahler manifolds with vanishing first Chern class

We investigate the deformation theory of a class of generalized calibrations in Riemannian manifolds for which the tangent bundle has reduced structure group U(n), SU(n), G_2 and Spin(7). For this we use the property of the associated calibration form to be parallel with respect to a metric connection which may have non-vanishing torsion. In all these cases, we find that if there is a moduli space, then it is finite dimensional. We present various examples of generalized calibrations that include almost hermitian manifolds with structure group U(n) or SU(n), nearly parallel G_2 manifolds and group manifolds. We find that some Hopf fibrations are deformation families of generalized calibrations. In addition, we give sufficient conditions for a hermitian manifold (M,g,J) to admit Chern and Bismut connections with holonomy contained in SU(n). In particular we show that any connected sum of $k \geq 3$ copies of $S^3 \times S^3$ admits a hermitian structure for which the restricted holonomy of a Bismut connection is contained in SU(3).Comment: 43 pages, Latex, typos corrected, reference added in section

Geometry and supersymmetry of heterotic warped flux AdS backgrounds

We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with $n\not=3$. Moreover the warp factor of AdS$_3$ backgrounds is constant, the geometry is a product $AdS_3\times M^7$ and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of $M^7$ has been specified in all cases. For 2 supersymmetries, it has been found that $M^7$ admits a suitably restricted $G_2$ structure. For 4 supersymmetries, $M^7$ has an $SU(3)$ structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, $M^7$ has an $SU(2)$ structure and can be described locally as a $S^3$ fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-K\"ahler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of $\alpha'$ corrections.Comment: 34 pages. Reference adde

All Killing Superalgebras for Warped AdS Backgrounds

We present all the symmetry superalgebras $\mathfrak{g}$ of all warped AdS$_k\times_w M^{d-k}$, $k>2$, flux backgrounds in $d=10, 11$ dimensions preserving any number of supersymmetries. First we give the conditions for $\mathfrak{g}$ to decompose into a direct sum of the isometry algebra of AdS$_k$ and that of the internal space $M^{d-k}$. Assuming this decomposition, we identify all symmetry superalgebras of AdS$_3$ backgrounds by showing that the isometry groups of internal spaces act transitively on spheres. We demonstrate that in type II and $d=11$ theories the AdS$_3$ symmetry superalgebras may not be simple and also present all symmetry superalgebras of heterotic AdS$_3$ backgrounds. Furthermore, we explicitly give the symmetry superalgebras of AdS$_k$, $k>3$, backgrounds and prove that they are all classical.Comment: 41 pages, late

High-temperature ferroelectric order and magnetic field-cooled effect driven magnetoelectric coupling in R2BaCuO5 (R= Er, Dy, Sm)

The high-temperature ferroelectric order and a remarkable magnetoelectric effect driven by the magnetic field cooling are reported in R2BaCuO5 (R = Er, Dy, Sm) series. The ferroelectric (FE) orders are observed at much higher temperatures than their magnetic orders for all three members. The value of FE Curie temperature (TFE) is considerably high as ~ 235 K with the polarization value (P) of ~ 1410 {\mu}C/m2 for a 4 kV/cm poling field in case of Er2BaCuO5, whereas the values of TFE and P are also promising as ~ 232 K and ~ 992 {\mu}C/m2 for Dy2BaCuO5, and ~ 184 K and ~ 980 {\mu}C/m2 for Sm2BaCuO5. The synchrotron diffraction studies of Dy2BaCuO5 confirm a structural transition at TFE to a polar Pna21 structure, which correlates the FE order. An unusual magnetoelectric coupling is observed below the R order for Er and Dy compounds and below the Cu order for Sm compound, when the pyroelectric current is recorded only with the magnetic field both in heating and cooling cycles i.e. typical magnetic field cooled effect. The magnetic field cooled effect driven emergence of polarization is ferroelectric in nature, as it reverses due to the opposite poling field. The unexplored R2BaCuO5 series attracts the community for large TFE, high P value, and strange magnetoelectric consequences.Comment: 9 figures and 2 supporting figure

Do supersymmetric anti-de Sitter black rings exist?

We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is that of the supersymmetric, topologically spherical, black hole solution of Chong et al. This proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity. However, we do find a solution corresponding to the near-horizon geometry of a supersymmetric black ring held in equilibrium by a conical singularity, which suggests that nonsupersymmetric anti-de Sitter black rings may exist but cannot be "balanced" in the supersymmetric limit.Comment: Latex, 18 pages, 1 figure. v2: minor change

HKT Geometry and Fake Five Dimensional Supergravity

Recent results on the relation between hyper-Kahler geometry with torsion and solutions admitting Killing spinors in minimal de sitter supergravity are extended to more general supergravity models with vector multiplets.Comment: 14 pages, latex. Minor typos corrected, references adde

Vanishing Preons in the Fifth Dimension

We examine supersymmetric solutions of N=2, D=5 gauged supergravity coupled to an arbitrary number of abelian vector multiplets using the spinorial geometry method. By making use of methods developed in hep-th/0606049 to analyse preons in type IIB supergravity, we show that there are no solutions preserving exactly 3/4 of the supersymmetry.Comment: 19 pages, latex. Reference added, and further modification to the introductio

Calibrated Entanglement Entropy

The Ryu-Takayanagi prescription reduces the problem of calculating entanglement entropy in CFTs to the determination of minimal surfaces in a dual anti-de Sitter geometry. For 3D gravity theories and BTZ black holes, we identify the minimal surfaces as special Lagrangian cycles calibrated by the real part of the holomorphic one-form of a spacelike hypersurface. We show that (generalised) calibrations provide a unified way to determine holographic entanglement entropy from minimal surfaces, which is applicable to warped AdS$_3$ geometries. We briefly discuss generalisations to higher dimensions.Comment: v1 22 pages, 1 figure; v2 appendix improved and moved into the body to show the application of calibrations to find minimal surfaces in warped AdS, matches published versio

Maximally Minimal Preons in Four Dimensions

Killing spinors of N=2, D=4 supergravity are examined using the spinorial geometry method, in which spinors are written as differential forms. By making use of methods developed in hep-th/0606049 to analyze preons in type IIB supergravity, we show that there are no simply connected solutions preserving exactly 3/4 of the supersymmetry.Comment: 18 pages. References added, comments added discussing the possibility of discrete quotients of AdS(4) preserving 3/4 supersymmetry

Finite N Index and Angular Momentum Bound from Gravity

We exactly compute the finite N index and BPS partition functions for N=4 SYM theory in a newly proposed maximal angular momentum limit. The new limit is not predicted from the superconformal algebra, but naturally arises from the supergravity dual. We show that the index does not receive any finite N corrections while the free BPS partition function does.Comment: 14 pages, v2: minor revisions, published versio