A focus on focal surfaces

We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal surface (degree, class, class of its hyperplane section, sectional genus and degrees of the nodal and cuspidal curve). We study in particular the congruences of chords to a smooth curve and the congruences of bitangents or flexes to a smooth surface. We find that they possess unexpected components in their focal surface, and conjecture that they are the only ones with this property.Comment: Plain TeX, 33 pages with no figure

Black hole - D-brane correspondence: An example

We explore the connection between D-branes and black holes in one particular case: a $D3$-brane compactified to four dimensions on $T^6/Z_3$. Using the $D$-brane boundary state description we show the equivalence with a double extremal N=2 black hole solution of four dimensional supergravity.Comment: 15 pages, LaTeX. Contribution by C. Nunez to the conference Quantum Gravity in the Southern Cone, Bariloche 7-10 January 1998; to appear in the proceeding

On CP Violation in Minimal Renormalizable SUSY SO(10) and Beyond

We investigate the role of CP phases within the renormalizable SUSY SO(10) GUT with one 10_H, one 126bar_H one 126_H and one 210_H Higgs representations and type II seesaw dominating the neutrino mass matrix. This framework is non trivially predictive in the fermionic sector and connects in a natural way the GUT unification of b and tau Yukawa couplings with the bi-large mixing scenario for neutrinos. On the other hand, existing numerical analysis claim that consistency with quark and charged lepton data prevents the minimal setup from reproducing the observed CP violation via the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We re-examine the issue and find by inspection of the fermion mass sum rules and a detailed numerical scan that, even though the CKM phase takes preferentially values in the second quadrant, the agreement of the minimal model with the data is actually obtained in a non negligible fraction of the parameter space. We then consider a recently proposed renormalizable extension of the minimal model, obtained by adding one chiral 120-dimensional Higgs supermultiplet. We show that within such a setup the CKM phase falls naturally in the observed range. We emphazise the robust predictivity of both models here considered for neutrino parameters that are in the reach of ongoing and future experiments.Comment: 9 pages, 6 figures. Two refs added, discussion expanded. To appear on Phys. Rev.

Transverse Lepton Polarization in Polarized W Decays

Calculations of transverse polarization of leptons in the decay $W\rightarrow l\nu$ with polarized $W$'s are presented. Planned accelerators will produce enough $W$'s for observation of the Standard Model contributions to this polarization. One loop corrections to the polarization are given; these are too small to be seen at presently available $W$ sources. The exchange of Majorons will contribute to these polarizations; these may provide limits on the couplings of these particles to leptons.Comment: 8 pages set in RevTex III and 4 uucompressed figures. This revised version studies polarization effects due to the exchange of charged Majoron doublet

Gauge/Gravity Correspondence from Open/Closed String Duality

We compute the annulus diagram corresponding to the interaction of a fractional D3 brane with a gauge field on its world-volume and a stack of N fractional D3 branes on the orbifolds C^2 /Z_2 and C^3/Z_2 x Z_2. We show that its logarithmic divergence can be equivalently understood as due either to massless open string states circulating in the loop or to massless closed string states exchanged between two boundary states. This follows from the fact that, under open/closed string duality, massless states in the open and closed string channels are matched into each other without mixing with massive states. This explains why the perturbative properties of many gauge theories living on the worldvolume of less supersymmetric and nonconformal branes have been recently obtained from their corresponding supergravity solution.Comment: LaTeX, 28 page

Trophic cascades and the transient keystone concept

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordApex predator reintroductions are commonly motivated by the imperative to restore populations and wider ecosystem function by precipitating trophic cascades that release basal species. Yet evidence for the existence of such cascades is often equivocal, particularly where consumptive interactions between apex and intermediate predators are weak or absent. Here, using a tri-trophic skate-crab-bivalve study-system, we find that non-consumptive interactions between apex skate and intermediate crabs cascade down to consumptive interactions between crabs and bivalves, significantly reducing bivalve mortality. However, skate only functioned as keystone where crabs foraged for bivalves in the absence of mature bivalve reef: where reef was present, bivalve mortality was not significantly different in the presence or absence of skate. By facilitating the establishment of basal species which, in turn, diminish apex-intermediate effects, the skate's keystone function is subject to negative regulation. Thus, we propose that keystone functionality can be transient with respect to environmental context. Our findings have two central implications for apex predator reintroductions and basic ecology: (i) species hitherto not considered as keystone may have the capacity to act as such transiently, and; (ii) keystones are known to regulate ecosystems, but transience implies that ecosystems can regulate keystone function.Natural Environment Research Council (NERC