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 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

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

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

Rare Decay Modes of Quarter BPS Dyons

The degeneracy of quarter BPS dyons in N=4 supersymmetric string theories is known to jump across walls of marginal stability on which a quarter BPS dyon can decay into a pair of half BPS dyons. We show that as long as the electric and magnetic charges of the original dyon are primitive elements of the charge lattice, the subspaces of the moduli space on which a quarter BPS dyon becomes marginally unstable against decay into a pair of quarter BPS dyons or a half BPS dyon and a quarter BPS dyon are of codimension two or more. As a result any pair of generic points in the moduli space can be connected by a path avoiding these subspaces and there is no jump in the spectrum associated with these subspaces.Comment: LaTeX file, 9 pages; v2: a minor logical error corrected with no change in the result

Recounting Dyons in N=4 String Theory

A recently discovered relation between 4D and 5D black holes is used to derive weighted BPS black hole degeneracies for 4D N=4 string theory from the well-known 5D degeneracies. They are found to be given by the Fourier coefficients of the unique weight 10 automorphic form of the modular group Sp(2,Z). This result agrees exactly with a conjecture made some years ago by Dijkgraaf, Verlinde and Verlinde.Comment: 5 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

On the dyon partition function in N=2 theories

We study the entropy function of two N =2 string compactifications obtained as freely acting orbifolds of N=4 theories : the STU model and the FHSV model. The Gauss-Bonnet term for these compactifications is known precisely. We apply the entropy function formalism including the contribution of this four derivative term and evaluate the entropy of dyons to the first subleading order in charges for these models. We then propose a partition function involving the product of three Siegel modular forms of weight zero which reproduces the degeneracy of dyonic black holes in the STU model to the first subleading order in charges. The proposal is invariant under all the duality symmetries of the STU model. For the FHSV model we write down an approximate partition function involving a Siegel modular form of weight four which captures the entropy of dyons in the FHSV model in the limit when electric charges are much larger than magnetic charges.Comment: 48 page