TY - JOUR

T1 - Dyonic black hole degeneracies in N = 4 string theory from Dabholkar-Harvey degeneracies

AU - Chowdhury, Abhishek

AU - Kidambi, Abhiram

AU - Murthy, Sameer

AU - Reys, Valentin

AU - Wrase, Timm

PY - 2020/10/1

Y1 - 2020/10/1

N2 - The degeneracies of single-centered dyonic 14-BPS black holes (BH) in Type II string theory on K3×T2 are known to be coefficients of certain mock Jacobi forms arising from the Igusa cusp form Φ10. In this paper we present an exact analytic formula for these BH degeneracies purely in terms of the degeneracies of the perturbative 12-BPS states of the theory. We use the fact that the degeneracies are completely controlled by the polar coefficients of the mock Jacobi forms, using the Hardy-Ramanujan-Rademacher circle method. Here we present a simple formula for these polar coefficients as a quadratic function of the 12-BPS degeneracies. We arrive at the formula by using the physical interpretation of polar coefficients as negative discriminant states, and then making use of previous results in the literature to track the decay of such states into pairs of 12-BPS states in the moduli space. Although there are an infinite number of such decays, we show that only a finite number of them contribute to the formula. The phenomenon of BH bound state metamorphosis (BSM) plays a crucial role in our analysis. We show that the dyonic BSM orbits with U-duality invariant ∆ < 0 are in exact correspondence with the solution sets of the Brahmagupta-Pell equation, which implies that they are isomorphic to the group of units in the order ℤ[|Δ|] in the real quadratic field ℚ(|Δ|). We check our formula against the known numerical data arising from the Igusa cusp form, for the first 1650 polar coefficients, and find perfect agreement.

AB - The degeneracies of single-centered dyonic 14-BPS black holes (BH) in Type II string theory on K3×T2 are known to be coefficients of certain mock Jacobi forms arising from the Igusa cusp form Φ10. In this paper we present an exact analytic formula for these BH degeneracies purely in terms of the degeneracies of the perturbative 12-BPS states of the theory. We use the fact that the degeneracies are completely controlled by the polar coefficients of the mock Jacobi forms, using the Hardy-Ramanujan-Rademacher circle method. Here we present a simple formula for these polar coefficients as a quadratic function of the 12-BPS degeneracies. We arrive at the formula by using the physical interpretation of polar coefficients as negative discriminant states, and then making use of previous results in the literature to track the decay of such states into pairs of 12-BPS states in the moduli space. Although there are an infinite number of such decays, we show that only a finite number of them contribute to the formula. The phenomenon of BH bound state metamorphosis (BSM) plays a crucial role in our analysis. We show that the dyonic BSM orbits with U-duality invariant ∆ < 0 are in exact correspondence with the solution sets of the Brahmagupta-Pell equation, which implies that they are isomorphic to the group of units in the order ℤ[|Δ|] in the real quadratic field ℚ(|Δ|). We check our formula against the known numerical data arising from the Igusa cusp form, for the first 1650 polar coefficients, and find perfect agreement.

KW - Black Holes in String Theory

KW - String Duality

KW - Superstrings and Heterotic Strings

KW - Supersymmetry and Duality

UR - http://www.scopus.com/inward/record.url?scp=85094190161&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2020)184

DO - 10.1007/JHEP10(2020)184

M3 - Article

AN - SCOPUS:85094190161

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 184

ER -