Abstract
AbstractThe degeneracies of 1/4 BPS states with unit torsion in heterotic string theory compactified on a six torus are given in terms of the Fourier coefficients of the reciprocal of the Igusa cusp Siegel modular form $$\Phi _{10}$$
Φ
10
of weight 10. We use the symplectic symmetries of the latter to construct a fine-grained Rademacher-type expansion which expresses these BPS degeneracies as a regularized sum over residues of the poles of $$1/\Phi _{10}$$
1
/
Φ
10
. The construction uses two distinct $$\textrm{SL}(2, {\mathbb {Z}})$$
SL
(
2
,
Z
)
subgroups of $$\textrm{Sp}(2, {\mathbb {Z}})$$
Sp
(
2
,
Z
)
which encode multiplier systems, Kloosterman sums and Eichler integrals appearing therein. Additionally, it shows how the polar data are explicitly built from the Fourier coefficients of $$1/\eta ^{24}$$
1
/
η
24
by means of a continued fraction structure.
Funder
Fundação para a Ciência e a Tecnologia
Universidade de Lisboa
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
Reference31 articles.
1. Dabholkar, A., Harvey, J.A.: Nonrenormalization of the superstring tension. Phys. Rev. Lett. 63, 478 (1989)
2. Dabholkar, A.: Exact counting of black hole microstates. Phys. Rev. Lett. 94, 241301 (2005). [arXiv:hep-th/0409148]
3. Maldacena, J.M., Moore, G.W., Strominger, A.: Counting BPS black holes in toroidal Type II string theory, arXiv:hep-th/9903163
4. Dijkgraaf, R., Verlinde, E.P., Verlinde, H.L.: Counting dyons in N=4 string theory. Nucl. Phys. B 484, 543–561 (1997). [arXiv:hep-th/9607026]
5. Shih, D., Strominger, A., Yin, X.: Recounting Dyons in N=4 string theory. JHEP 10, 087 (2006). [arXiv:hep-th/0505094]