Comments on the spectrum of CHL dyons

Abstract

Abstract:We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with N = 4 supersymmetry. The partition function for these dyons is given in terms of Siegel modular forms associated with genus-two Riemann surfaces. We point out a subtlety in demonstrating S-duality invariance of the resulting degeneracies and give a prescription that makes the invariance manifest. We show, using M-theory lift of string webs, that the genus-two contribution captures the degeneracy only if a specific irreducibility criterion is satisfied by the charges. Otherwise, in general there can be additional contributions from higher genus Riemann surfaces. We analyze the negative discriminant states predicted by the formula. We show that even though there are no big black holes in supergravity corresponding to these states, there are multi-centered particle-like configurations with subleading entropy in agreement with the microscopic prediction and our prescription for S-duality invariance. The existence of the states is moduli dependent and we exhibit the curves of marginal stability and comment on its relation to S-duality invariance.

Dyon death eaters

“…[10] that the quantum states of such dyons are not counted by the famous genus-2 modular form of ref. [15] but appear to be connected to a higher-genus Riemann surface.…”

Heat kernels on the AdS2 cone and logarithmic corrections to extremal black hole entropy

“…For fields on AdS2 ⊗ S 2 /ZN which we encounter in section 5 we shall indeed treat the zero mode integral separately. 12 It is easy to see that for a given ℓ = N p + q, where 0 ≤ q < N is an integer, the allowed m values are |m| = 0, N, 2N, . .…”

Mixed Rademacher and BPS black holes

“…For instance, a more intricate case to examine is the one of Type IIB string theory compactified on K3 × T 2 . The counting function of 1/4-BPS states (dyons) which are stable throughout the compactification's moduli space in this theory [9][10][11][12][13][14][15][16] is related to mixed mock Jacobi forms [17]. The mixed-mock character of these functions is a consequence of the wall-crossing phenomenon and implies that the 1/4-BPS states counting problem can be translated into the question of recovering the exact Fourier coefficients of certain mixed mock Jacobi forms.…”