Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories

The spectrum of quarter BPS dyons in N=4 supersymmetric string theories can change as the asymptotic moduli cross walls of marginal stability on which the dyon can break apart into a pair of half BPS states. In this paper we classify these marginal stability walls and examine this phenomenon in the context of exact dyon spectrum found in a class of N=4 supersymmetric string theories. We argue that the dyon partition functions in different domains separated by marginal stability walls are the same, but the choice of integration contour needed for extracting the degeneracies from the partition function differ in these different regions. We also find that in the limit of large charges the change in the degeneracy is exponentially suppressed compared to the leading contribution. This is consistent with the fact that in the computation of black hole entropy we do not encounter any change as the asymptotic moduli fields move across the walls of marginal stability. Finally we carry out some tests of S-duality invariance in the theory.Comment: LateX file, 1 figure, 42 pages; v2 more tests of S-duality added with complete proof for all N<7; v3: minor change

Adding Charges to N=4 Dyons

The spectrum of dyons in a class of N=4 supersymmetric string theories has been found for a specific set of electric and magnetic charge vectors. We extend the analysis to more general charge vectors by considering various charge carrying collective excitations of the original system.Comment: LaTeX file, 16 page

Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds

We find the exact spectrum of a class of quarter BPS dyons in a generic N=4 supersymmetric Z_N orbifold of type IIA string theory on K3\times T^2 or T^6. We also find the asymptotic expansion of the statistical entropy to first non-leading order in inverse power of charges and show that it agrees with the entropy of a black hole carrying same set of charges after taking into account the effect of the four derivative Gauss-Bonnet term in the effective action of the theory.Comment: LaTeX file, 39 pages; minor change

SWOT Analysis of the horticultural farms in the Plovdiv region of Bulgaria

Agriculture/horticulture has traditionally been an important sector in the economy of Bulgaria. This paper reviews the changes in agriculture/horticulture in the Plovdiv region of Bulgaria after 1989 when the transition towards a free market economy began. In particular, it provides a review of the internal capabilities (strengths and weaknesses) of the horticultural farms and the impact upon them of the external environment (opportunities and threats). While many farmers regarded their experience as a strength, farmers having farms of different size identified additional different strengths, and different weaknesses and opportunities. Whereas, all of them were influenced by similar threats and the relative importance of these perceived threats did not varied depending upon the size of the farm

Degeneracy of Decadent Dyons

A quarter-BPS dyon in $\mathcal{N}=4$ super Yang-Mills theory is generically `decadent' in that it is stable only in some regions of the moduli space and decays on submanifolds in the moduli space. Using this fact, and from the degeneracy of the system close to the decay, a new derivation for the degeneracy of such dyons is given. The degeneracy obtained from these very simple physical considerations is in precise agreement with the results obtained from index computations in all known cases. Similar considerations apply to dyons in $\mathcal{N}=2$ gauge theories. The relation between the $\mathcal{N} =4$ field theory dyons and those counted by the Igusa cusp form in toroidally compactified heterotic string is elucidated.Comment: Some typos corrected and references adde

Status of major southern California marine sport fish species with management recommendations, based on analyses of catch and size composition data collected on board commercial passenger fishing vessels from 1985 through 1987

This report on the status of major southern California marine sport fish species, together with management recommendations, is based on analyses of catch and size composition data, which were collected on board Commercial Passenger Fishing Vessels (CPFV) from 1985 through 1987. The project was designed to determine the status of those fishes that support the CPFV industry, and to make management recommendations when deemed necessary. We collected and analyzed data based on random, stratified, on-board sampling of weekday (excluding holidays), open CPFV's on a year-round basis. We sampled 1/2-day, 3/4-day, and full-day type trips at a level of 5%. The survey area extended from below the United States-Mexican border to Point Arguello. Catch estimates were extrapolated to include weekday as well as weekend and holiday, open and chartered CPFV's. We sampled 736 CPFV trips in 1985, 650 in 1986, and 631 in 1987. We encountered 180 species of fishes, including 49 species of rockfishes. We performed detailed analyses on 14 non-rockfish species and 12 rockfish species, as well as all fishes as a group and all rockfishes as a group. We found a moderate increase in total catch of combined fish species between this study and one in the mid-1970's, due primarily to sizeable increases in catches of Pacific mackerel, kelp bass, barred sand bass, and barracuda. However, we also found that there has been more than a 50% decline in the CPFV rockfish catches, due primarily to substantial decreases in catches of bocaccio, chilipepper, and olive rockfish. We have recommended that the current 15-rockfish bag limit regulation be reduced to a 10-rockfish bag limit, and that additional and equitable conservation measures also be implemented on the commercial rockfish fishery. (385pp.

Dyon Death Eaters

We study general two-body decays of primitive and non-primitive 1/4-BPS dyons in four-dimensional type IIB string compactifications. We find a ``master equation'' for marginal stability that generalises the curve found by Sen for half-BPS decay, and analyse this equation in a variety of cases including decays to 1/4-BPS products. For half-BPS decays, an interesting and useful relation is exhibited between walls of marginal stability and the mathematics of Farey sequences and Ford circles. We exhibit an example in which two curves of marginal stability intersect in the interior of moduli space.Comment: 24 pages, 1 figure, v2: section on non-primitive dyons slightly modified and expanded, few other small change

The mixed black hole partition function for the STU model

We evaluate the mixed partition function for dyonic BPS black holes using the recently proposed degeneracy formula for the STU model. The result factorizes into the OSV mixed partition function times a proportionality factor. The latter is in agreement with the measure factor that was recently conjectured for a class of N=2 black holes that contains the STU model.Comment: 14 page

Three String Junction and N=4 Dyon Spectrum

The exact spectrum of dyons in a class of N=4 supersymmetric string theories gives us information about dyon spectrum in N=4 supersymmetric gauge theories. This in turn can be translated into prediction about the BPS spectrum of three string junctions on a configuration of three parallel D3-branes. We show that this prediction agrees with the known spectrum of three string junction in different domains in the moduli space separated by walls of marginal stability.Comment: LaTeX file, 14 page

Two Centered Black Holes and N=4 Dyon Spectrum

The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy of two centered small black holes which disappear as we cross the walls of marginal stability.Comment: LaTeX file, 12 pages; v3: added footnote 2 regarding overall sign of the index, expanded footnote 3, added reference