103 research outputs found
Supersymmetric Standard Model, Branes and Del Pezzo Surfaces
No full textThe Standard Model of particle physics is one of the most important successful results of the work of the last century physicists. In this new book, the authors present topical research in the study of new developments in the Standard Model. Topics discussed include non-equilibrium theory, fractional dynamics and the physics of the terascale sector; unexplored regions in QFT and the conceptual foundations of the Standard Model; supersymmetric Standard Model, Branes and Del Pezzo surfaces; fermion condensate as Higgs substitute and Lepton flavor violation shedding light on CP-violation.
Even though the Standard Model of particles has been confirme by several experiments, many questions require improvements. Beyond the problem of Grand Unification the mass gap problem, the question of hierarchies, low boson masses and dynamical soft supersymmetry breaking, there is the really hard difficult in including gravity in a full quantum paradigm of the Standard Model. The most famous scheme elaborated in order to solve the last and, possibly, all this points is String Theory.
Dualities, mirror symmetry, M-theory and AdS/CFT are some of the powerful tools
which permit to perform several progresses in all the mentioned directions, at least in principle. However, interactions of String Theory with phenomenology are really recent results. A way to get a contact between theory and phenomenology is the so called bottom-up approach. We will present here a possible String Theory approach to the (Minimal Supersymmetric) Standard Model based on the geometric engineering construction firs proposed in [H. Verlinde and M. Wijnholt, JHEP 0701, 106]. We will study the relevant geometry along the lines of [S.L. Cacciatori and M. Compagnoni, JHEP 1005:078,2010], and the related physics. We will study the singular orbifold C3/27, with 27 a suitable non abelian group, its geometry and show how it can be desingularized. To render technical computations as simple as possible we will work also with a simplifie toric version, studing its main properties at K-theory level, and we will discuss how such calculations should be extended to the non abelian case. The associated relevant physics will be discussed
Projective superspaces in practice
No full textThis paper is devoted to the study of supergeometry of complex projective superspaces Pn|m. First, we provide formulas for the cohomology of invertible sheaves of the form OPn|m(l), that are pullbacks of ordinary invertible sheaves on the reduced variety Pn. Next, by studying the even Picard group Pic0(Pn|m), classifying invertible sheaves of rank 1|0, we show that the sheaves OPn|m(l) are not the only invertible sheaves on Pn|m, but there are also new genuinely supersymmetric invertible sheaves that are unipotent elements in the even Picard group. We study the Π-Picard group PicΠ(Pn|m), classifying Π-invertible sheaves of rank 1|1, proving that there are also non-split Π-invertible sheaves on supercurves P1|m. Further, we investigate infinitesimal automorphisms and first order deformations of Pn|m, by studying the cohomology of the tangent sheaf using a supersymmetric generalisation of the Euler exact sequence. A special attention is paid to the meaningful case of supercurves P1|mand of Calabi–Yau's Pn|n+1. Last, with an eye to applications to physics, we show in full detail how to endow P1|2with the structure of N=2 super Riemann surface and we obtain its SUSY-preserving infinitesimal automorphisms from first principles, that prove to be the Lie superalgebra osp(2|2). A particular effort has been devoted to keep the exposition as concrete and explicit as possible
The Dirac equation in Kerr-Newman-AdS black hole background
No full textWe consider the Dirac equation on the Kerr–Newman–AdS black hole background. We first perform the variable separation for the Dirac equation and define the Hamiltonian operator H. Then we show that for a massive Dirac field with mass \mu \geq 1 / ͑(2l), where l is linked to the cosmological constant \Lambda by \Lambda = -3 /(l^2), essential self-adjointness of H on
C_0^\infty ((r_+ ,\infty)\times S^2͒)^4 is obtained even in presence of the boundarylike behavior of infinity in an asymptotically AdS black hole background. Furthermore, qualitative spectral properties of the Hamiltonian are taken into account and in agreement with the existing results concerning the case of stationary axisymmetric asymptotically flat black holes we infer the absence of time-periodic and normalizable solutions of the Dirac equation around the black hole in the nonextremal case
D-branes on C^3_6. Part I: prepotential and GW-invariants
No full textThis is the first of a set of papers having the aim to provide a detailed description of brane configurations on a family of noncompact threedimensional Calabi-Yau manifolds. The starting point is the singular manifold C^3/Z_6, which admits five distinct crepant resolutions. Here we apply local mirror symmetry to partially determine the prepotential encoding the GW-invariants of the resolved varieties. It results that such prepotential provides all numbers but the ones corresponding to curves having null intersection with the compact divisor. This is realized by means of a conjecture, due to S. Hosono, so that our results provide a check confirming at least in part the conjecture
On the geometry of C^3/\Delta_{27} and del Pezzo surfaces
No full textWe clarify some aspects of the geometry of a resolution of the orbifold X = C3/Δ27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of Δ27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient
Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
No full textThe behavior of a charged massive Dirac field on a Reissner–Nordstrom–AdS
black hole background is investigated. We first analyze the problem of the
essential self-adjointness of the Dirac Hamiltonian, which is made difficult by
the boundary-like behavior of spatial infinity, and we find that the Hamiltonian
is essentially self-adjoint iff \mu L \geq 1/2; moreover, we determine the essential
spectrum of the Hamiltonian. Then we focus on the analysis of the discharge
problem for the case \mu L \geq 1/2. We follow the Ruffini–Damour–Deruelle
approach and, as in the standard Reissner–Nordstrom black hole case, we
find that the existence of level-crossing between the positive and negative
energy solutions of the Dirac equation is at the root of the pair-creation process
associated with the discharge of the black hole
Analogous Hawking Effect in Dielectric Media and Solitonic Solutions
No full textWe review some aspects of our longstanding research concerning the analogous Hawking effect in dispersive dielectric media. We introduce nonlinear contributions in the polarization field in the relativistically covariant version of the Hopfield model and then, in order to provide a simplified description aimed at avoiding some subtleties in the quantization of the original model, we discuss the so-called -model. We show that the nonlinearity allows for introducing in a self-consistent way the otherwise phenomenological dependence of the susceptibility and of the resonance frequency on the spacetime variables, and this is a consequence of the linearization of the model around solitonic solutions representing propagating perturbations of the refractive index, to be then associated with the Hawking effect
Discrete Matter, Far Fields, and Dark Matter
No full textWe show that in cosmology the gravitational action of the far away matter has quite relevant effects, if retardation of the forces and discreteness of matter (with its spatial correlation) are taken into account. The expansion rate is found to be determined by the density of the far away matter, i.e., by the density of matter at remote times. This leads to the introduction of an effective density, which has to be five times larger than the present one, if the present expansion rate is to be accounted for. The force per unit mass on a test particle is found to be of the order of 0.2 cH 0. The corresponding contribution to the virial of the forces for a cluster of galaxies is also discussed, and it is shown that it fits the observations if a decorrelation property of the forces at two separated points is assumed. So it appears that the gravitational effects of the far away matter may have the same order of magnitude as the corresponding local effects of dark matter
Experimental quantum cosmology in time-dependent optical media
No full textIt is possible to construct artificial spacetime geometries for light by using intense laser pulses that modify the spatiotemporal properties of an optical medium. Here we theoretically investigate experimental possibilities for studying spacetime metrics of the form . By tailoring the laser pulse shape and medium properties, it is possible to create a refractive index variation that can be identified with . Starting from a perturbative solution to a generalized Hopfield model for the medium described by an , we provide estimates for the number of photons generated by the time-dependent spacetime. The simplest example is that of a uniformly varying that therefore describes the Robertson–Walker metric, i.e. a cosmological expansion. The number of photon pairs generated in experimentally feasible conditions appears to be extremely small. However, large photon production can be obtained by periodically modulating the medium and thus resorting to a resonant enhancement similar to that observed in the dynamical Casimir effect. Curiously, the spacetime metric in this case closely resembles that of a gravitational wave. Motivated by this analogy, we show that a periodic gravitational wave can indeed act as an amplifier for photons. The emission for an actual gravitational wave will be very weak but should be readily observable in the laboratory analogue
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