Abstract
We study three properties of 1/4 BPS dyons at small charges in string compactifications which preserve mathcal{N} = 4 supersymmetry. We evaluate the non-trivial constant present in the one loop statistical entropy for mathcal{N} = 4 compactifications of type IIB theory on K3 × T2 orbifolded by an order ℤN freely acting orbifold g′ including all CHL compactifications. This constant is trivial for the un-orbifolded model but we show that it contributes crucially to the entropy of low charge dyons in all the orbifold models. We then show that the meromorphic Jacobi form which captures the degeneracy of 1/4 BPS states for the first two non-trivial magnetic charges can be decomposed into an Appell-Lerch sum and a mock Jacobi form transforming under Γ0(N). This generalizes the earlier observation of Dabholkar-Murthy-Zagier to the orbifold models. Finally we study the sign of the Fourier coefficients of the inverse Siegel modular form which counts the index of 1/4 BPS dyons in mathcal{N} = 4 models obtained by freely acting ℤ2 and ℤ3 orbifolds of type II theory compactified on T6. We show that sign of the index for sufficiently low charges and ensuring that it counts single centered black holes, violates the positivity conjecture of Sen which indicates that these states posses non-trivial hair.
Highlights
Given the success of the microscopic formula for the degeneracies of dyons in the large charge limit, it is natural to study its properties for dyons with small charges
We study three properties of 1/4 BPS dyons at small charges in string compactifications which preserve N = 4 supersymmetry
We show that the meromorphic Jacobi form which captures the degeneracy of 1/4 BPS states for the first two non-trivial magnetic charges can be decomposed into an AppellLerch sum and a mock Jacobi form transforming under Γ0(N )
Summary
The weights of the Siegel modular forms corresponding to the twisted elliptic genera constructed in this paper is listed in table 2. Using the twisted elliptic genera and product form for the Siegel modular form in (2.3) we can obtain d(Q, P ) as defined by its Fourier expansion in (2.1) for low values of the charges. We will perform this comparison for low values of charges as it is clear that for very large values of charges this constant will not play a relevant role Such a comparison for low values of charges of the one loop statistical entropy function with the exact entropy was made for the un-orbifolded K3 × T 2 compactification in [6] and later in [10]. It was seen that the statistical entropy function at one loop agrees with the exact entropy to 2% even for the lowest admissible charge We will extend this comparison for all the orbifolds g listed in table 1. We will see that the constant C1 is non-trivial and depends on the orbifold and contributes crucially towards Ss(t1a)t
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
