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Dyonic black hole degeneracies in N $$ \mathcal{N} $$ = 4 string theory from Dabholkar-Harvey degeneracies
- Source :
- Journal of High Energy Physics, Vol 2020, Iss 10, Pp 1-59 (2020), Journal of High Energy Physics
- Publication Year :
- 2020
- Publisher :
- SpringerOpen, 2020.
-
Abstract
- The degeneracies of single-centered dyonic $\frac14$-BPS black holes (BH) in Type II string theory on K3$\times T^2$ are known to be coefficients of certain mock Jacobi forms arising from the Igusa cusp form $\Phi_{10}$. In this paper we present an exact analytic formula for these BH degeneracies purely in terms of the degeneracies of the perturbative $\frac12$-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 $\frac12$-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 $\frac12$-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 $\Delta<br />Comment: 58 pages, 9 figures, 3 tables
- Subjects :
- High Energy Physics - Theory
Nuclear and High Energy Physics
Type II string theory
FOS: Physical sciences
String theory
01 natural sciences
Superstrings and Heterotic Strings
0103 physical sciences
Black Holes in String Theory
FOS: Mathematics
lcsh:Nuclear and particle physics. Atomic energy. Radioactivity
Number Theory (math.NT)
Invariant (mathematics)
010306 general physics
Mathematical physics
Physics
Mathematics - Number Theory
010308 nuclear & particles physics
Order (ring theory)
Cusp form
Moduli space
High Energy Physics - Theory (hep-th)
Supersymmetry and Duality
lcsh:QC770-798
Quadratic field
String Duality
String duality
Subjects
Details
- Language :
- English
- ISSN :
- 10298479
- Volume :
- 2020
- Issue :
- 10
- Database :
- OpenAIRE
- Journal :
- Journal of High Energy Physics
- Accession number :
- edsair.doi.dedup.....c0510242960d7c857c51d61c77976d9f