Moduli stabilization with open and closed string fluxes

We study the stabilization of all closed string moduli in the T^6/Z_2 orientifold, using constant internal magnetic fields and 3-form fluxes that preserve N=1 supersymmetry in four dimensions. We first analyze the stabilization of Kahler class and complex structure moduli by turning on magnetic fluxes on different sets of D9 branes that wrap the internal space T^6/Z_2. We present explicit consistent string constructions, satisfying in particular tadpole cancellation, where the radii can take arbitrarily large values by tuning the winding numbers appropriately. We then show that the dilaton-axion modulus can also be fixed by turning on closed string constant 3-form fluxes, consistently with the supersymmetry preserved by the magnetic fields, providing at the same time perturbative values for the string coupling. Finally, several models are presented combining open string magnetic fields that fix part of Kahler class and complex structure moduli, with closed string 3-form fluxes that stabilize the remaining ones together with the dilaton.Comment: 49 pages, a new model added, as well as improvements and reference

Magnetic fluxes and moduli stabilization

Stabilization of closed string moduli in toroidal orientifold compactifications of type IIB string theory are studied using constant internal magnetic fields on D-branes and 3-form fluxes that preserve N=1 supersymmetry in four dimensions. Our analysis corrects and extends previous work by us, and indicates that charged scalar VEV's need to be turned on, in addition to the fluxes, in order to construct a consistent supersymmetric model. As an explicit example, we first show the stabilization of all Kahler class and complex structure moduli by turning on magnetic fluxes on different sets of D9-branes that wrap the internal space T^6 in a compactified type I string theory, when a charged scalar on one of these branes acquires a non-zero VEV. The latter can also be determined by adding extra magnetized branes, as we demonstrate in a subsequent example. In a different model with magnetized D7-branes, in a IIB orientifold on T^6/Z_2, we show the stabilization of all the closed string moduli, including the axion-dilaton at weak string coupling g_s, by turning on appropriate closed string 3-form fluxes.Comment: v2: minor changes, added discussio

High Speed Blanking: An Experimental Method to Measure Induced Cutting Forces

Lien vers la version éditeur: http://link.springer.com/article/10.1007/s11340-013-9738-1A new blanking process that involves punch speed up to 10 ms −1 has obvious advantages in increased productivity. However, the inherent dynamics of such a process makes it difficult to develop a practical high speed punch press. The fracture phenomenon governing the blanking process has to be well understood to correctly design the machine support and the tooling. To observe this phenomenon at various controlled blanking speeds a specific experimental device has been developed. The goal is to measure accurately the shear blanking forces imposed on the specimen during blanking. In this paper a new method allowing the blanking forces to be measured and taking into account the proposed test configuration is explained. This technique has been used to determine the blanking forces experienced when forming C40 steel and quantifies the effect of process parameters such as punch die clearance, punch speed, and sheet metal thickness on the blanking force evolution

Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity

We show that the n-fold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the "Ising class", or n-fold integrals from enumerative combinatorics, like lattice Green functions, are actually diagonals of rational functions. As a consequence, the power series expansions of these solutions of linear differential equations "Derived From Geometry" are globally bounded, which means that, after just one rescaling of the expansion variable, they can be cast into series expansions with integer coefficients. Besides, in a more enumerative combinatorics context, we show that generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions. We give a large set of results illustrating the fact that the unique analytical solution of Calabi-Yau ODEs, and more generally of MUM ODEs, is, almost always, diagonal of rational functions. We revisit Christol's conjecture that globally bounded series of G-operators are necessarily diagonals of rational functions. We provide a large set of examples of globally bounded series, or series with integer coefficients, associated with modular forms, or Hadamard product of modular forms, or associated with Calabi-Yau ODEs, underlying the concept of modularity. We finally address the question of the relations between the notion of integrality (series with integer coefficients, or, more generally, globally bounded series) and the modularity (in particular integrality of the Taylor coefficients of mirror map), introducing new representations of Yukawa couplings.Comment: 100 page

Globally nilpotent differential operators and the square Ising model

We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their lambda-extensions. These integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations. These differential operators are very selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing on the factorised parts of all these operators, we find out that the global nilpotence of the factors corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, and even a remarkable weight-1 modular form emerging in the three-particle contribution $\chi^{(3)}$ of the magnetic susceptibility of the square Ising model. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or $\infty$) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new structures associated with simple deformations of the nilpotent property.Comment: 55 page

Renormalization, isogenies and rational symmetries of differential equations

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group.Comment: 36 page

Painleve versus Fuchs

The sigma form of the Painlev{\'e} VI equation contains four arbitrary parameters and generically the solutions can be said to be genuinely ``nonlinear'' because they do not satisfy linear differential equations of finite order. However, when there are certain restrictions on the four parameters there exist one parameter families of solutions which do satisfy (Fuchsian) differential equations of finite order. We here study this phenomena of Fuchsian solutions to the Painlev{\'e} equation with a focus on the particular PVI equation which is satisfied by the diagonal correlation function C(N,N) of the Ising model. We obtain Fuchsian equations of order $N+1$ for C(N,N) and show that the equation for C(N,N) is equivalent to the $N^{th}$ symmetric power of the equation for the elliptic integral $E$. We show that these Fuchsian equations correspond to rational algebraic curves with an additional Riccati structure and we show that the Malmquist Hamiltonian $p,q$ variables are rational functions in complete elliptic integrals. Fuchsian equations for off diagonal correlations $C(N,M)$ are given which extend our considerations to discrete generalizations of Painlev{\'e}.Comment: 18 pages, Dedicated to the centenary of the publication of the Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

Linear electro optic coefficients r13 and r33 of in barium-calcium-titanate crystals doped with rhodium (BaxCa1-xTiO3 : Rh) at 633nm and 850nm

We present the electro optic properties of rhodium-doped barium calcium titanate (BCT) crystals of the congruent melting composition Ba0.77Ca0.23TiO3, in carrying out two types of measurements: electro optic (EO) and absorption. The studied coefficients are r13 and r33 as ordinary and extraordinary waves are involved respectively, the polarized absorption spectra of rhodium-doped barium-calcium-titanate (Rh: BCT) are recorded from 400nm to 1100nm. We propose an experimental investigation of the EO coefficients, for two different wavelengths corresponding to strong and weak absorption, based on an interferometric set-up. A static electric field is applied out the sample under study, leading to the measurement of the r13 and r33 coefficients. While the phase transition is shifted to the low temperature in compared with BaTiO3 the electro optic coefficients save a high values. Because of the phase transition at low temperatures the values of the coefficients are high compared with BaTiO3.We present the electro optic properties of rhodium-doped barium calcium titanate (BCT) crystals of the congruent melting composition Ba0.77Ca0.23TiO3, in carrying out two types of measurements: electro optic (EO) and absorption. The studied coefficients are r13 and r33 as ordinary and extraordinary waves are involved respectively, the polarized absorption spectra of rhodium-doped barium-calcium-titanate (Rh: BCT) are recorded from 400nm to 1100nm. We propose an experimental investigation of the EO coefficients, for two different wavelengths corresponding to strong and weak absorption, based on an interferometric set-up. A static electric field is applied out the sample under study, leading to the measurement of the r13 and r33 coefficients. While the phase transition is shifted to the low temperature in compared with BaTiO3 the electro optic coefficients save a high values. Because of the phase transition at low temperatures the values of the coefficients are high compared with BaTiO3