60 research outputs found
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
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
Spectrum of CHL Dyons from Genus-Two Partition Function
We compute the genus-two chiral partition function of the left-moving
heterotic string for a CHL orbifold. The required twisted
determinants can be evaluated explicitly in terms of the untwisted determinants
and theta functions using orbifold techniques. The dependence on Prym periods
cancels neatly once summation over odd charges is properly taken into account.
The resulting partition function is a Siegel modular form of level two and
precisely equals recently proposed dyon partition function for this model. This
result provides an independent weak coupling derivation of the dyon partition
function using the M-theory lift of string webs representing the dyons. We
discuss generalization of this technique to general orbifolds.Comment: 25 pages, 2 figures, minor typos correcte
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
Degeneracy of Decadent Dyons
A quarter-BPS dyon in 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 gauge theories. The relation between the
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
Dyon Spectrum in N=4 Supersymmetric Type II String Theories
We compute the spectrum of quarter BPS dyons in freely acting Z_2 and Z_3
orbifolds of type II string theory compactified on a six dimensional torus. For
large charges the result for statistical entropy computed from the degeneracy
formula agrees with the corresponding black hole entropy to first non-leading
order after taking into account corrections due to the curvature squared terms
in the effective action. The result is significant since in these theories the
entropy of a small black hole, computed using the curvature squared corrections
to the effective action, fails to reproduce the statistical entropy associated
with elementary string states.Comment: LaTeX file, 32 pages; v2:minor change
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
Dying Dyons Don't Count
The dyonic 1/4-BPS states in 4D string theory with N=4 spacetime
supersymmetry are counted by a Siegel modular form. The pole structure of the
modular form leads to a contour dependence in the counting formula obscuring
its duality invariance. We exhibit the relation between this ambiguity and the
(dis-)appearance of bound states of 1/2-BPS configurations. Using this insight
we propose a precise moduli-dependent contour prescription for the counting
formula. We then show that the degeneracies are duality-invariant and are
correctly adjusted at the walls of marginal stability to account for the
(dis-)appearance of the two-centered bound states. Especially, for large black
holes none of these bound states exists at the attractor point and none of
these ambiguous poles contributes to the counting formula. Using this fact we
also propose a second, moduli-independent contour which counts the "immortal
dyons" that are stable everywhere.Comment: 27 pages, 2 figures; one minus sign correcte
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
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