Dyon death eaters

Abstract

Abstract: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 1 2 -BPS decay, and analyse this equation in a variety of cases including decays to 1 4 -BPS products. For 1 2 -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.

Black hole entropy function, attractors and precision counting of microstates

“…Our analysis will follow the one given in [168]. Some related work can be found in [150,167,169,170]. Let us consider a state carrying electric charge Q and magnetic charge P and examine under what condition it can decay into a pair of half-BPS states.…”

“…Since for half BPS states the electric and magnetic charges must be parallel, these pair of states must have charge vectors of the form (a M, c M) and (b N , d N ) for some constants a, b, 35 There are also subspaces of the asymptotic moduli space where the mass of a quarter BPS state becomes equal to the sum of the masses of a pair of quarter BPS states, or a quarter BPS state and a half-BPS state or more than two half or quarter BPS states. However it has been shown in [169,170] that such subspaces are of codimension larger than one. Hence in going from one generic point in the moduli space to another one can avoid them by going around them.…”

How do black holes predict the sign of the Fourier coefficients of siegel modular forms?

“…5 Since we shall always consider the range in which Q 2 , P 2 > 0, (Q.P) 2 < Q 2 P 2 (non-singular supersymmetric black holes exist only in this range) we must have Q.P ≥ 0. (3.5) Since the equations for the other walls of R are also known [53,57] we can use similar method to determine the condition on the charges which will ensure that the attractor point lies inside R. But we shall now describe a simpler method for determining this using S-duality transformation that acts simultaneously on the charges and the τ -moduli as Similarly mapping the wall from 1 to i∞ to the wall from 0 to i∞ by the transformation τ = τ − 1 we get the third condition Q.P ≤ P 2 . Together with these three conditions we must add the conditions Q 2 , P 2 , {Q 2 P 2 − (Q.P) 2 } > 0 since classical black hole solutions with non-singular event horizon exists only when this condition is satisfied.…”

Threel string junction and 𝒩 = 4 dyon spectrum

“…As we vary the asymptotic moduli the degeneracy can actually jump across walls of marginal stability, -codimension one subspaces of the moduli space on which the original quarter BPS dyon can decay into a pair of half-BPS dyons [13,14,16,17,26,27]. As has been reviewed in detail in [18], a very useful way to label a given wall of marginal stability is to specify the relation between the charges of the decay products and the charges of the original state.…”

“…This allows us to compare a BPS state of the configuration described above with that of the SU(3) gauge theory that arises as the low energy limit of heteroric string theory on T 4 × T 2 . For this we first need to learn how to translate a charge vector of the type given in (27) to the one given in (1). We do this by comparing the charges carried by the massive gauge fields.…”