Tachyon mass, c-function and Counting localized degrees of freedom

We discuss the localized tachyon condensation in the non-supersymmetric orbifold theories by taking the cosmological constant as the measure of degrees of freedom (d.o.f). We first show asymptotic density of state is not a proper quantity to count the 'localized' d.o.f. We then show that localized d.o.f lead us a c-function given by the lightest tachyon mass, which turns out to be the same as the tachyon potential recently suggested by Dabholkar and Vafa. We also argue that delocalized d.o.f also encode information on the process of localized tachyon condensation in the g-function, based on the fact that the global geometry of the orbifolds is completely determined by the local geometry around the fixed points. For type II, both c- and g-function respect the stability of the supersymmetric models and both allow all the process suggested by Adams, Polchinski and Silverstein.Comment: 15 pages, 2 figures, v2: typo corrected, reference added. v3: abstract stretche

Catholic Schools and Multicultural Education: A Good Match

This article reflects on the place of multicultural education in Catholic schools. The authors review the history and development of Catholic schools in order to set a context for examination of the appropriateness of multicultural education

Catholic Schools and Multicultural Education: A Good Match

This article reflects on the place of multicultural education in Catholic schools. The authors review the history and development of Catholic schools in order to set a context for examination of the appropriateness of multicultural education

Chiral rings and GSO projection in Orbifolds

The GSO projection in the twisted sector of orbifold background is sometimes subtle and incompatible descriptions are found in literatures. Here, from the equivalence of partition functions in NSR and GS formalisms, we give a simple rule of GSO projection for the chiral rings of string theory in \C^r/\Z_n, $r=1,2,3$. Necessary constructions of chiral rings are given by explicit mode analysis.Comment: 24 page

Bats and Water: Anthropogenic Alterations Threaten Global Bat Populations

Natural bodies of open water in desert landscapes, such as springs and ephemeral pools, and the plant-life they support, are important resources for the survival of animals in hyper arid, arid and semi-arid (dryland) environments. Human-made artificial water sources, i.e. waste-water treatment ponds, catchments and reservoirs, have become equally important for wildlife in those areas. Bodies of open water are used by bats either for drinking and/or as sites over which to forage for aquatic emergent insects. Due to the scarcity of available water for replenishing water losses during roosting and flight, open bodies of water of many shapes and sizes may well be a key resource influencing the survival, activity, resource use and the distribution of insectivorous bats. In this chapter, we review the current knowledge of bats living in semi- and arid regions around the world and discuss the factors that influence their richness, behaviour and activity around bodies of water. We further present how increased anthropogenic changes in hydrology and water availability may influence the distribution of species of bats in desert environments and offer directions for future research on basic and applied aspects on bats and the water they use in these environments

Condensation of Tubular D2-branes in Magnetic Field Background

It is known that in the Minkowski vacuum a bunch of IIA superstrings with D0-branes can be blown-up to a supersymmetric tubular D2-brane, which is supported against collapse by the angular momentum generated by crossed electric and magnetic Born-Infeld (BI) fields. In this paper we show how the multiple, smaller tubes with relative angular momentum could condense to a single, larger tube to stabilize the system. Such a phenomena could also be shown in the systems under the Melvin magnetic tube or uniform magnetic field background. However, depending on the magnitude of field strength, a tube in the uniform magnetic field background may split into multiple, smaller tubes with relative angular momentum to stabilize the system.Comment: Latex 10 pages, mention the dynamical joining of the tubes, modify figure

On the quantum stability of IIB orbifolds and orientifolds with Scherk-Schwarz SUSY breaking

We study the quantum stability of Type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken {\it \`a la} Scherk-Schwarz (SS) by twisting periodicity conditions along a circle of radius R. In particular, we compute the R-dependence of the one-loop induced vacuum energy density $\rho(R)$, or cosmological constant. For SS twists different from Z2 we always find, for both orbifolds and orientifolds, a monotonic $\rho(R)<0$, eventually driving the system to a tachyonic instability. For Z2 twists, orientifold models can have a different behavior, leading either to a runaway decompactification limit or to a negative minimum at a finite value R_0. The last possibility is obtained for a 4D chiral orientifold model where a more accurate but yet preliminary analysis seems to indicate that $R_0\to \infty$ or towards the tachyonic instability, as the dependence on the other geometric moduli is included.Comment: 26 pages, 5 figures; v2: version to appear in Nucl.Phys.

Orientifolds of String Theory Melvin backgrounds

We study the dynamics of type I strings on Melvin backgrounds, with a single or multiple twisted two-planes. We construct two inequivalent types of orientifold models that correspond to (non-compact) irrational versions of Scherk-Schwarz type breaking of supersymmetry. In the first class of vacua, D-branes and O-planes are no longer localized in space-time but are smeared along the compact Melvin coordinate with a characteristic profile. On the other hand, the second class of orientifolds involves O-planes and D-branes that are both rotated by an angle proportional to the twist. In case of ``multiple Melvin spaces'', some amount of supersymmetry is recovered if the planes are twisted appropriately and part of the original O-planes are transmuted into new ones. The corresponding boundary and crosscap states are determined.Comment: 34 pages, LaTe

D-Brane Probe and Closed String Tachyons

We consider a D-brane probe in unstable string background associated with flux branes. The twist in spacetime metric reponsible for the supersymmetry breaking is shown to manifest itself in mixing of open Wilson lines with the phases of some adjoint matter fields, resulting in a nonlocal and nonsupersymmetric form of Yang-Mills theory as the probe dynamics. This provides a setup where one can study fate of a large class of unstable closed string theories that include as a limit type 0 theories and various orbifolds of type II and type 0 theories. We discuss the limit of ${\bf C}/Z_n$ orbifold in some detail and speculate on couplings with closed string tachyons.Comment: LaTeX, 17 pages, typos fixed, references update

(Twisted) Toroidal Compactification of pp-Waves

The maximally supersymmetric type IIB pp-wave is compactified on spatial circles, with and without an auxiliary rotational twist. All spatial circles of constant radius are identified. Without the twist, an S$^1$ compactification can preserve 24, 20 or 16 supercharges. $T^2$ compactifications can preserve 20, 18 or 16 supercharges; $T^3$ compactifications can preserve 18 or 16 supercharges and higher compactifications preserve 16 supercharges. The worldsheet theory of this background is discussed. The T-dual and decompactified type IIA and M-theoretic solutions which preserve 24 supercharges are given. Some comments are made regarding the AdS parent and the CFT description.Comment: 22 pages REVTeX 4 and AMSLaTeX. v3: References and a paragraph on nine dimensional Killing spinors were added. v4: A few typos corrected and a footnote was modifie