Calabi-Yau 3-folds from 2-folds

We consider type IIA string theory on a Calabi-Yau 2-fold with D6-branes wrapping 2-cycles in the 2-fold. We find a complete set of conditions on the supergravity solution for any given wrapped brane configuration in terms of SU(2) structures. We reduce the problem of finding a supergravity solution for the wrapped branes to finding a harmonic function on R$\times$CY$_2$. We then lift this solution to 11-dimensions as a product of R$^{(4.1)}$ and a Calabi-Yau 3-fold. We show how the metric on the 3-fold is determined in terms of the wrapped brane solution. We write down the distinguished (3,0) form and the K{\"a}hler form of the 3-fold in terms of structures defined on the base 2-d complex manifold. We discuss the topology of the 3-fold in terms of the D6-branes and the underlying 2-fold. We show that in addition to the non-trivial cycles inherited from the underlying 2-fold there are $N-1$ new 2-cycles. We construct closed (1,1) forms corresponding to these new cycles. We also display some explicit examples. One of our examples is that of D6-branes wrapping the 2-cycle in an A$_1$ ALE space, the resulting 3-fold has $h^{(1,1)}=N$, where $N$ is the number of D6-branes.Comment: 30 page

Dramatic robustness of a multiple delay dispersed interferometer to spectrograph errors: how mixing delays reduces or cancels wavelength drift

We describe demonstrations of remarkable robustness to instrumental noises by using a multiple delay externally dispersed interferometer (EDI) on stellar observations at the Hale telescope. Previous observatory EDI demonstrations used a single delay. The EDI (also called “TEDI”) boosted the 2,700 resolution of the native TripleSpec NIR spectrograph (950-2450 nm) by as much as 10x to 27,000, using 7 overlapping delays up to 3 cm. We observed superb rejection of fixed pattern noises due to bad pixels, since the fringing signal responds only to changes in multiple exposures synchronous to the applied delay dithering. Remarkably, we observed a ~20x reduction of reaction in the output spectrum to PSF shifts of the native spectrograph along the dispersion direction, using our standard processing. This allowed high resolution observations under conditions of severe and irregular PSF drift otherwise not possible without the interferometer. Furthermore, we recently discovered an improved method of weighting and mixing data between pairs of delays that can theoretically further reduce the net reaction to PSF drift to zero. We demonstrate a 350x reduction in reaction to a native PSF shift using a simple simulation. This technique could similarly reduce radial velocity noise for future EDI’s that use two delays overlapped in delay space (or a single delay overlapping the native peak). Finally, we show an extremely high dynamic range EDI measurement of our ThAr lamp compared to a literature ThAr spectrum, observing weak features (~0.001x height of nearest strong line) that occur between the major lines. Because of individuality of each reference lamp, accurate knowledge of its spectrum between the (unfortunately) sparse major lines is important for precision radial velocimetry

Signature of superconducting states in cubic crystal without inversion symmetry

The effects of absence of inversion symmetry on superconducting states are investigated theoretically. In particular we focus on the noncentrosymmetric compounds which have the cubic symmetry $O$ like Li$_2$Pt$_3$B. An appropriate and isotropic spin-orbital interaction is added in the Hamiltonian and it acts like a magnetic monopole in the momentum space. The consequent pairing wavefunction has an additional triplet component in the pseudospin space, and a Zeeman magnetic field $\bf{B}$ can induce a collinear supercurrent $\bf{J}$ with a coefficient $\kappa(T)$. The effects of anisotropy embedded in the cubic symmetry and the nodal superconducting gap function on $\kappa(T)$ are also considered. From the macroscopic perspectives, the pair of mutually induced $\bf{J}$ and magnetization ${\bf{M}}$ can affect the distribution of magnetic field in such noncentrosymmetric superconductors, which is studied through solving the Maxwell equation in the Meissner geometry as well as the case of a single vortex line. In both cases, magnetic fields perpendicular to the external ones emerge as a signature of the broken symmetry.Comment: 16 pages in pre-print forma

Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

We study the electric flux tubes that undertake color confinement in N=2 supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U(1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid" type II phase. Also, ratios among string tensions are seen to follow no simple pattern. We examine the situation at the half Higgsed vacua and find evidence for solutions with the behaviour of superconducting strings. In some cases they are solutions to BPS equations.Comment: 15 pages, 1 figure, revtex; v2: typos corrected, final versio

Let's Twist Again: General Metrics of G(2) Holonomy from Gauged Supergravity

We construct all complete metrics of cohomogeneity one G(2) holonomy with S^3 x S^3 principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a non-trivial embedding of the special Lagrangian three-cycle wrapped by the D6-branes in the lower dimensional supergravity. There are constraints that neatly reduce the general ansatz to a six functions one. Within this approach, the Hitchin system and the flop transformation are nicely realized in eight dimensional gauged supergravity.Comment: 31 pages, latex; v2: minor changes, references adde

New non compact Calabi-Yau metrics in D=6

A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric depend on only one complex coordinate of the hyperkahler 4-dimensional space and its complex conjugated. This situation in particular gives a dual description of D6-branes wrapping a complex 1-cycle inside the hyperkahler space, which was studied by Fayyazuddin. The present work generalize the construction given by him. But the explicit solutions we present correspond to the non linear problem. This is a non linear equation with respect to two variables which, with the help of some specific anzatz, is reduced to a non linear equation with a single variable solvable in terms of elliptic functions. In these terms we construct an infinite family of non compact Calabi-Yau metrics.Comment: A numerical error has been corrected together with the corresponding analysis of the metri

High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: part 2, photon noise theory

High-resolution broadband spectroscopy at near-infrared (NIR) wavelengths (950 to 2450 nm) has been performed using externally dispersed interferometry (EDI) at the Hale telescope at Mt. Palomar, with the TEDI interferometer mounted within the central hole of the 200-in. primary mirror in series with the comounted TripleSpec NIR echelle spectrograph. These are the first multidelay EDI demonstrations on starlight. We demonstrated very high (10×) resolution boost and dramatic (20× or more) robustness to point spread function wavelength drifts in the native spectrograph. Data analysis, results, and instrument noise are described in a companion paper (part 1). This part 2 describes theoretical photon limited and readout noise limited behaviors, using simulated spectra and instrument model with noise added at the detector. We show that a single interferometer delay can be used to reduce the high frequency noise at the original resolution (1× boost case), and that except for delays much smaller than the native response peak half width, the fringing and nonfringing noises act uncorrelated and add in quadrature. This is due to the frequency shifting of the noise due to the heterodyning effect. We find a sum rule for the noise variance for multiple delays. The multiple delay EDI using a Gaussian distribution of exposure times has noise-to-signal ratio for photon-limited noise similar to a classical spectrograph with reduced slitwidth and reduced flux, proportional to the square root of resolution boost achieved, but without the focal spot limitation and pixel spacing Nyquist limitations. At low boost (∼1×) EDI has ∼1.4× smaller noise than conventional, and at >10× boost, EDI has ∼1.4× larger noise than conventional. Readout noise is minimized by the use of three or four steps instead of 10 of TEDI. Net noise grows as step phases change from symmetrical arrangement with wavenumber across the band. For three (or four) steps, we calculate a multiplicative bandwidth of 1.8:1 (2.3:1), sufficient to handle the visible band (400 to 700 nm, 1.8:1) and most of TripleSpec (2.6:1)

Magnetoelectric effects in heavy-fermion superconductors without inversion symmetry

We investigate effects of strong electron correlation on magnetoelectric transport phenomena in noncentrosymmetric superconductors with particular emphasis on its application to the recently discovered heavy-fermion superconductor CePt$_3$Si. Taking into account electron correlation effects in a formally exact way, we obtain the expression of the magnetoelectric coefficient for the Zeeman-field-induced paramagnetic supercurrent, of which the existence was predicted more than a decade ago. It is found that in contrast to the usual Meissner current, which is much reduced by the mass renormalization factor in the heavy-fermion state, the paramagnetic supercurrent is not affected by the Fermi liquid effect. This result implies that the experimental observation of the magnetoelectric effect is more feasible in heavy-fermion systems than that in conventional metals with moderate effective mass.Comment: 8 pages, 2 figures, minor correction

Chern-Simons Vortices in Supergravity

We study supersymmetric vortex solutions in three-dimensional abelian gauged supergravity. First, we construct the general U(1)-gauged D=3, N=2 supergravity whose scalar sector is an arbitrary Kahler manifold with U(1) isometry. This construction clarifies the connection between local supersymmetry and the specific forms of some scalar potentials previously found in the literature -- in particular, it provides the locally supersymmetric embedding of the abelian Chern-Simons Higgs model. We show that the Killing spinor equations admit rotationally symmetric vortex solutions with asymptotically conical geometry which preserve half of the supersymmetry.Comment: 26 pages, LaTeX2