A note on Kahler potential of charged matter in F-theory

We study the Kahler potential of charged matter fields, whose profiles have a peak on their matter curve — on an “intersection” of 7-branes, in an F-theory compactification. It is shown that the Kahler potential is exactly given by the integral over the matter curve, but not by the integral over the whole GUT surface of 7-branes.     

From local to global in F-theory model building

When locally engineering F-theory models some D7$D7$-branes for the gauge group factors are specified and matter is localized on the intersection curves of the compact parts of the world-volumes. In this note, we discuss to what extent one can draw conclusions about F-theory models by just restricting the attention locally to a particular seven-brane. Globally, the possible D7$D7$-branes are not independent from each other and the (compact part of the) D7$D7$-brane can have unavoidable intrinsic singularities. Many special intersecting loci which were not chosen by hand occur inevitably, notably codimension-three loci which are not   intersections of matter curves. We describe these complications specifically in a global SU(5)$SU\left(5\right)$ model and also their impact on the tadpole cancellation condition.     

Intersecting brane models and F-theory in six dimensions

We analyze six-dimensional supergravity theories coming from intersecting brane models on the toroidal orbifold T⁴/_Z2$T^4/{\mathbb{Z}}_2$. We use recently developed tools for mapping general 6D supergravity theories to F-theory to identify F-theory constructions dual to the intersecting brane models. The F-theory picture illuminates several aspects of these models. In particular, we have some new insight into the matter spectrum on intersecting branes, and analyze gauge group enhancement as branes approach orbifold points. These novel features of intersecting brane models are also relevant in four dimensions, and are confirmed in 6D using more standard Chan–Paton methods.     

Classifying bases for 6D F-theory models

We classify six-dimensional F-theory compactifications in terms of simple features of the divisor structure of the base surface of the elliptic fibration. This structure controls the minimal spectrum of the theory. We determine all irreducible configurations of divisors (??clusters??) that are required to carry nonabelian gauge group factors based on the intersections of the divisors with one another and with the canonical class of the base. All 6D F-theory models are built from combinations of these irreducible configurations. Physically, this geometric structure characterizes the gauge algebra and matter that can remain in a 6D theory after maximal Higgsing. These results suggest that all 6D supergravity theories realized in F-theory have a maximally Higgsed phase in which the gauge algebra is built out of summands of the types su(3), so(8), f₄, e₆, e₈, e₈, (g₂ ?? su(2)); and su(2) ?? so(7) ?? su(2), with minimal matter content charged only under the last three types of summands, corresponding to the non-Higgsable cluster types identified through F-theory geometry. Although we have identified all such geometric clusters, we have not proven that there cannot be an obstruction to Higgsing to the minimal gauge and matter configuration for any possible F-theory model. We also identify bounds on the number of tensor fields allowed in a theory with any fixed gauge algebra; we use this to bound the size of the gauge group (or algebra) in a simple class of F-theory bases.     

A note on thermal models

The “thermal models” are discussed in general in thermodynamic context, and then predictions of some hadronisation models are compared to each other and to experimental results at 20+200 GeV/N beam energy.     

A note on state decomposition independent local invariants

We present a method to change the fluorescence contrast between two dyes with high fluorescence anisotropy in the same solution under different polarization directions by using polarization-shaped pulses. First a theoretical relationship between contrast, anisotropy and polarization is derived for this case. Then the wavelength dependent polarization anisotropy and the change of contrast by phase-shaping for a solution of Rhodamine B and Stilbene 3 in glycerol is shown. Finally, the application of the polarization-shaped pulses is demonstrated.     

A note on local unitary equivalence of isotropic-like states

We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.     

SUSY and GUT threshold effects in SUSYSU(5) models

We study consequences of the threshold effects of supersymmetric (SUSY) and superheavy (GUT) particles to the gauge coupling unification condition in two specific supersymmetricSU(5) models, the minimal model and the missing doublet model with natural doublet-triplet splitting. We present a consistent treatment of theSU(2)×U(1) breaking mass terms in the SUSY particle threshold effects, as well as that of the top quark threshold effect, which have been ignored in previous works. The GUT threshold effects are constrained by the proton decay experiments and by some theoretical consistency conditions, but they are strongly model dependent. For example, under a certain assumption for the SUSY particle masses, the minimal model favors a large (>1 TeV) SUSY breaking scale or a high _s(m _z )(<0.12), whereas=" the=" missing=" doublet=" model=" allows=" a=" low="><1 tev)=" susy=" breaking=" scale=" for=" 0.11=">_s(m _z )>0.13. The consequences of these two models in the proton decay experiments are also briefly discussed.     

Inflation in SU(5) GUT models coupled to gravity

We have examined the SU(5) GUT phase transition in (nearly) Coleman-Weinberg type models coupled to gravity and have found three different modes through which the transition may proceed, depending upon the choice of (zero temperature) parameters. For each of these modes, we have determined numerically whether there is sufficient inflation to explain some long standing cosmological puzzles, and we find that this is the case only in a very restricted region of parameter space.     

A note on a local effect at the Schwarzschild sphere

Passage of the Schwarzschild radius is shown to be locally measurable by a sign change in a certain scalar. In the Kerr solution this scalar changes sign at the stationary limit. This is an example of the use of a coordinate-invariant method, based on the curvature tensor and a finite number of its covariant derivatives, for investigating gravitational fields.     

A note on the dynamic boundary conditions in Munk-like circulation models

The present note deals with Munk's ocean model and proposes an alternative approach to find its solution, with special regard to the western boundary layer. We introduce a suitable “distance” between the related Sverdrup streamfunction and all the admissible streamfunctions which are valid in the western boundary layer. We prove that such distance has a minimum that singles out a unique solution. Unlike the traditional method, this procedure works without assuming a priori any dynamic boundary condition. Received 16 July 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: fulcri@itt.ts.cnr.it     

A note on vector flux models for radiation dose calculations

This paper reviews and extends modelling of anisotropic fluxes for radiation belt protons to provide closed-form equations for vector proton fluxes and proton flux anisotropy in terms of standard omnidirectional flux models. These equations provide a flexible alternative to the data-based vector flux models currently available. At higher energies, anisotropy of trapped proton flux in the upper atmosphere depends strongly on the variation of atmospheric density with altitude. Calculations of proton flux anisotropies using present models require specification of the average atmospheric density along trapped particle trajectories and its variation with mirror point altitude. For an isothermal atmosphere, calculations show that in a dipole magnetic field, the scale height of this trajectory-averaged density closely approximates the scale height of the atmosphere at the mirror point of the trapped particle. However, for the earth's magnetic field, the altitudes of mirror points vary for protons drifting in longitude. This results in a small increase in longitude-averaged scale heights compared to the atmospheric scale heights at minimum mirror point altitudes. The trajectory-averaged scale heights are increased by about 10-20% over scale heights from standard atmosphere models for protons mirroring at altitudes less than 500 km in the South Atlantic Anomaly. Atmospheric losses of protons in the geomagnetic field minimum in the South Atlantic Anomaly control proton flux anisotropies of interest for radiation studies in low earth orbit. Standard atmosphere models provide corrections for diurnal, seasonal and solar activity-driven variations. Thus, determination of an "equilibrium" model of trapped proton fluxes of a given energy requires using a scale height that is time-averaged over the lifetime of the protons. The trajectory-averaged atmospheric densities calculated here lead to estimates for trapped proton lifetimes. These lifetimes provide appropriate time-averaging intervals for equilibrium models of trapped proton fluxes.