Supersymmetric backgrounds from generalized Calabi–Yau manifolds

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kähler form e^iJ and the holomorphic form Ω. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: e^iJ is closed under the action of the twisted exterior derivative in IIA theory, and similarly Ω is closed in IIB. This means that supersymmetric SU(3)-structure manifolds are always complex in IIB while they are twisted symplectic in IIA. Modulo a different action of the B-field, these are all generalized Calabi–Yau manifolds, as defined by Hitchin. To cite this article: M. Graña et al., C. R. Physique 5 (2004).

Résumé

On montre que les transformations de supersymétrie pour les théories des cordes de type II peuvent être traduites dans des équations différentielles pour une paire de spineurs purs, l'exponentiel de la forme de Kähler e^iJ et la forme holomorphe Ω. Ces équations sont symétriques sous l'échange des deux spineurs purs et des formes de RR de rang pair ou impair. Cette propriété est la symétrie miroir pour les variétés avec torsion. On voit aussi que les fluxes de RR entrent seulement dans une des deux équations : e^iJ est fermé sous l'action de la dérivée extérieure « twisted » dans la corde de type IIA, et de la même manière Ω est fermé en type IIB. Cela implique que les variétés supersymétriques de structure SU(3) sont toujours complexes en type IIB ou bien symplectiques « twisted » en IIA. Ces variétés sont donc des variétés des Calabi–Yau généralisées selon la définition de Hitchin, mais avec une action du champ B différente. Pour citer cet article : M. Graña et al., C. R. Physique 5 (2004).     

Arithmetic of Calabi–Yau varieties and rational conformal field theory

It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of Calabi–Yau manifolds and the underlying conformal field theory. Specifically, it is pointed out how the algebraic number field determined by the fusion rules of the conformal field theory can be derived from the number theoretic structure of the cohomological Hasse–Weil L-function determined by Artin’s congruent zeta function of the algebraic variety. In this context, a natural number theoretic characterization arises for the quantum dimensions in this geometrically determined algebraic number field.     

Exceptional Calabi–Yau spaces: the geometry of backgrounds with flux

In this paper we define the analogue of Calabi–Yau geometry for generic , flux backgrounds in type II supergravity and M‐theory. We show that solutions of the Killing spinor equations are in one‐to‐one correspondence with integrable, globally defined structures in generalised geometry. Such “exceptional Calabi–Yau” geometries are determined by two generalised objects that parametrise hyper‐ and vector‐multiplet degrees of freedom and generalise conventional complex, symplectic and hyper‐Kähler geometries. The integrability conditions for both hyper‐ and vector‐multiplet structures are given by the vanishing of moment maps for the “generalised diffeomorphism group” of diffeomorphisms combined with gauge transformations. We give a number of explicit examples and discuss the structure of the moduli spaces of solutions. We then extend our construction to and flux backgrounds preserving eight supercharges, where similar structures appear, and finally discuss the analogous structures in generalised geometry.     

(MS)SM‐like models on smooth Calabi‐Yau manifolds from all three heterotic string theories

We perform model searches on smooth Calabi‐Yau compactifications for both the supersymmetric E₈ × E₈ and SO(32) as well as for the non‐supersymmetric SO(16) × SO(16) heterotic strings simultaneously. We consider line bundle backgrounds on both favorable CICYs with relatively small h₁₁ and the Schoen manifold. Using Gram matrices we systematically analyze the combined consequences of the Bianchi identities and the tree‐level Donaldson‐Uhlenbeck‐Yau equations inside the Kähler cone. In order to evaluate the model building potential of the three heterotic theories on the various geometries, we perform computer‐aided scans. We have generated a large number of GUT‐like models (up to over a few hundred thousand on the various geometries for the three heterotic theories) which become (MS)SM‐like upon using a freely acting Wilson line. For all three heterotic theories we present tables and figures summarizing the potentially phenomenologically interesting models which were obtained during our model scans.     

Relative periods and open-string integer invariants for a compact Calabi–Yau hypersurface

In this work we compute relative periods for B-branes, realized in terms of divisors in a compact Calabi–Yau hypersurface, by means of direct integration. Although we exemplify the method of direct integration with a particular Calabi–Yau geometry, the recipe automatically generalizes for divisors in other Calabi–Yau geometries as well. From the calculated relative periods we extract double-logarithmic periods. These periods qualify to describe disk instanton generated N=1 superpotentials of the corresponding compact mirror Calabi–Yau geometry in the large volume regime. Finally we extract the integer invariants encoded in these brane superpotentials.     

Line bundle twisted chiral de Rham complex,chiral Riemann-Roch formula and D-branes on toric manifolds

I present the results of the elliptic genus calculations in various examples of twisted chiral de Rham complex on one- and two-dimensional toric compact manifolds. The explicit calculations are made for line bundle twisted chiral de Rham complex on ?¹, ?² and Hirzebruch surface. Based on these results I propose the elliptic genus expression of the bundle twisted chiral de Rham complex for general smooth compact two dimensional toric manifold. The expression resembles Riemann-Roch formula and coincides with the later in certain limit. I interpret the result in terms of infinite tower of open string oscillator contributions and identify directly the open string boundary conditions of the corresponding bound state of D-branes.     

Characteristic polynomials of random Hermitian matrices and Duistermaat–Heckman localisation on non-compact Kähler manifolds

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N×N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard “supersymmetry” approach, we integrate out Grassmann variables at the early stage and circumvent the use of the Hubbard–Stratonovich transformation in the “bosonic” sector. The method, suggested recently by J.V. Fyodorov [Nucl. Phys. B 621 [PM] (2002) 643], is shown to be capable of calculation when reinforced with a generalisation of the Itzykson–Zuber integral to a non-compact integration manifold. We arrive to such a generalisation by discussing the Duistermaat–Heckman localisation principle for integrals over non-compact homogeneous Kähler manifolds. In the limit of large-N the asymptotic expression for the correlation function reproduces the result outlined earlier by A.V. Andreev and B.D. Simons [Phys. Rev. Lett. 75 (1995) 2304].     

Moduli stabilization, large-volume dS minimum without -branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi–Yau's

We consider two sets of issues in this paper. The first has to do with moduli stabilization, existence of “area codes” [A. Giryavets, New attractors and area codes, JHEP 0603 (2006) 020, hep-th/0511215] and the possibility of getting a non-supersymmetric dS minimum without the addition of -branes as in KKLT for type II flux compactifications. The second has to do with the “inverse problem” [K. Saraikin, C. Vafa, Non-supersymmetric black holes and topological strings, hep-th/0703214] and “fake superpotentials” [A. Ceresole, G. Dall'Agata, Flow equations for non-BPS extremal black holes, JHEP 0703 (2007) 110, hep-th/0702088] for extremal (non-)supersymmetric black holes in type II compactifications. We use (orientifold of) a “Swiss cheese” Calabi–Yau [J.P. Conlon, F. Quevedo, K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 0508 (2005) 007, hep-th/0505076] expressed as a degree-18 hypersurface in WCP⁴[1,1,1,6,9] in the “large-volume-scenario” limit [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi–Yau flux compactifications, JHEP 0503 (2005) 007, hep-th/0502058]. The main result of our paper is that we show that by including non-perturbative α^′ and instanton corrections in the Kähler potential and superpotential [T.W. Grimm, Non-perturbative corrections and modularity in N=1 type IIB compactifications, arXiv: 0705.3253 [hep-th]], it may be possible to obtain a large-volume non-supersymmetric dS minimum without the addition of anti-D3 branes a la KKLT. The chosen Calabi–Yau has been of relevance also from the point of other studies of Kähler moduli stabilization via non-perturbative instanton contributions [F. Denef, M.R. Douglas, B. Florea, Building a better racetrack, JHEP 0406 (2004) 034, hep-th/0404257] and non-supersymmetric AdS vacua (and their subsequent dS-uplifts) using (α^′)³ corrections to the Kähler potential [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi–Yau flux compactifications, JHEP 0503 (2005) 007, hep-th/0502058; K. Becker, M. Becker, M. Haack, J. Louis, Supersymmetry breaking and alpha'-corrections to flux induced potentials, JHEP 0206 (2002) 060, hep-th/0204254; A. Westphal, de Sitter string vacua from Kähler uplifting, JHEP 0703 (2007) 102, hep-th/0611332; V. Balasubramanian, P. Berglund, Stringy corrections to Kähler potentials, SUSY breaking, and the cosmological constant problem, JHEP 0411 (2004) 085, hep-th/0408054].     

Effect of substituent on the UV–Vis spectra: an extension from disubstituted to multi‐substituted benzylideneanilines

For studying the substituent effects on the ν_max of substituted benzylideneanilines (XBAYs) systematically, 12 samples of 3,3′‐disubstituted XBAYs and 52 samples of multi‐substituted XBAYs were synthesized, and the substituent effects on their ν_max were investigated in this paper. A modified regression equation quantifying the ν_max of 4,4′/4,3′/3,4′/3,3′‐disubstituted and multi‐substituted XBAYs (shown as Eq. 3 ) was obtained. The results showed that the substituent effects on the ν_max of 3,3′‐substituted and multi‐substituted XBAYs became more complicated. In Eq. 3 , the contributions of the meta‐parameters to the ν_max of XBAYs were different from those of the corresponding para‐parameters. For the substituent cross‐interaction effects, there is no difference whatever the substituents are at meta‐position or para‐position. Compared with Eq. 1 , Eq. 3 obtained in this paper has a wider application and more accuracy in quantifying the ν_max of substituted XBAYs. Copyright © 2016 John Wiley & Sons, Ltd.     

Visible to NIR absorbing C–N and C–C bonding squaraines: A computational study

We report a comparative computational study of 2 series of molecules with C–N bonding squaraines (NSQ) and C–C bonding squaraines (CSQ), having absorption from visible to near infrared region (350‐800 nm). The NSQ are considered as molecules with break‐in conjugation, and CSQ are considered as molecules with complete conjugation in molecular backbone. The lowest electronic excitations in CSQ molecules are always having around 200 nm red shifted absorption than its corresponding NSQ molecules. The reason for this drastic red shift in CSQ series than NSQ has been systematically studied by density functional theory, time‐dependent density functional theory, and symmetry adopted cluster configuration interaction methods. The CSQ series are showing less charge transfer than NSQ, but having small diradical character. This study may be helpful in design and synthesis of new squaraine dyes, which are useful in materials applications.     

On the photoemission from III–V, ternary and quaternary materials: Simplified theory and relative comparison

We study theoretically the electron energy spectrum and the photoemission from III–V, ternary and quaternary materials in the presence of light waves, whose unperturbed energy band structures are defined by the three-band model of Kane. The band gap of semiconductors increases as a consequence of incident light waves and we have suggested two new experimental methods of determining the band gap of semiconductors in the presence of photoexcitations. The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings in the presence of external photoexcitation. It has been found taking n-InAs, n-InSb, n-Hg_1−xCd_xTe and n-In_1−xGa_xAs_yP_1−y lattice matched to InP, as examples that the photoemission increases with the increase in electron concentration and decreases in increasing intensity, wavelength and alloy composition, respectively, in various manners. The numerical values of the photoemission in the presence of light waves is less than that of the same for unperturbed three- and two-band models of Kane together with parabolic energy bands for all types of external variables. The strong dependence of the photoemission on the light intensity reflects the direct signature of light waves on the dispersion relation of the conduction electrons, which is in contrast when compared with the corresponding bulk specimens for the unperturbed band models. The rate of change is totally band structure dependent and is significantly influenced by the presence of the different energy band constants. The well-known result of the photoemission from non-degenerate wide gap materials has been obtained as a special case of the present analysis under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. Besides, we have suggested six important applications of our results in this context.     

An evaluation of surface properties and frictional forces generated from Al–Mo–Ni coating on piston ring

Surface properties of the Al–Mo–Ni coating plasma sprayed on the piston ring material and the frictional forces obtained by testing carried out under different loads, temperatures and frictional conditions were evaluated.

Al–Mo–Ni composite material was deposited on the AISI 440C test steel using plasma spraying method. The coated and uncoated samples were tested by being exposed to frictional testing under dry and lubricated conditions. Test temperatures of 25, 100, 200, and 300 °C and loads of 83, 100, 200, and 300 N were applied during the tests in order to obtain the frictional response of the coating under conditions similar to real piston ring/cylinder friction conditions. Gray cast iron was used as a counterface material. All the tests were carried out with a constant sliding speed of 1 m/s.

The properties of the coating were determined by using EDX and SEM analyses. Hardness distribution on the cross-section of the coating was also determined. In addition, the variations of the surface roughness after testing with test temperatures and loads under dry and lubricated conditions were recorded versus sliding distance.

It was determined that the surface roughness increased with increasing loads. It increased with temperature up to 200 °C and then decreased at 300 °C under dry test conditions.

Under lubricated conditions, the roughness decreased under the loads of 100 N and then increased. The roughness decreased at 200 °C but below and above this point it increased with the test temperature.

Frictional forces observed under dry and lubricated test conditions increased with load at running-in period of the sliding. The steady-state period was then established with the sliding distance as a normal situation. However, the frictional forces were generally lower at a higher test temperature than those at a lower test temperature. Surprisingly, the test temperature of 200 °C was a critical point for frictional forces and surface roughness.     

Oxygen self-diffusion in single-crystal MgO: secondary-ion mass spectrometric analysis with comparison of results from gas–solid and solid–solid exchange

Self-diffusion coefficients for ¹⁸O in single-crystal MgO have been determined from a novel specimen comprising an epitaxial layer of high-purity Mg¹⁸O upon a single crystal substrate of normal MgO. Heating the specimen in air produced a gas–solid exchange gradient at the sample surface as ¹⁸O in the epitaxial layer exchanged with ¹⁶O in air. A solid–solid interdiffusion gradient was produced between the substrate crystal and the ¹⁸O-enriched epitaxial layer. SIMS analysis of gas–solid exchange gradients prepared in the temperature range 1000–1650 °C provided diffusion coefficients that could be described as

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. Interdiffusion gradients produced by annealing at 1100 and 1200 °C yielded the self-diffusion coefficients that were comparable to those obtained from gas–solid exchange, indicating that the surface exchange reaction is fast enough. The results are interpreted in terms of a defect model in which oxygen diffusion occurs by an interstitial type of defect as a result of suppression of anion vacancy concentration by large concentrations of extrinsic cation vacancies.     

Indirect carbon–carbon spin–spin couplings across one,two and three bonds in pyridine and diazine systems: experiment and theory

An excellent linear correlation is found between a large body of experimental spin–spin carbon–carbon couplings, J(CC), across one, two and three bonds in pyridine and diazine ring systems and the corresponding B3PW91/6‐311++G(d,p)//B3PW91/6‐311++G(d,p) computations. The correlation does not differ significantly from the simplest relationship possible, J(CC)_exp. = J(CC)_calcd., within a small and random spread of about 1 Hz. There are 276 experimental values considered, and 124 out of these are new and come from the present work. The aromatic carbon–carbon couplings vary from ?7.6 through +78.5 Hz. It is shown that the correlation provides a reliable tool for predictions of the signs of aromatic J(CC)'s even if the magnitudes of the latter are of the order of 1 Hz. It is demonstrated, for the first time, that the relatively weak ² J(CC) couplings, in the heteroaromatic systems studied, can bear either sign and span a considerable range of about 11 Hz. The character of the correlation indicates that rovibronic effects on aromatic J(CC)'s and those of nuclear motions on aromatic J(CC)'s are practically negligible. All of this is in a perfect agreement with our recent extensive studies on aromatic J(CC)'s in analogous benzene ring system. Substituent effects on the aromatic J(CC)'s turn out to be significant not only for ¹J(CC)'s but also for most of ³J(CC)'s and ² J(CC)'s, and the computation neatly reciprocates these trends. Copyright © 2008 John Wiley & Sons, Ltd.