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Rademacher Expansion of a Siegel Modular Form for N=4 Counting.

Authors :
Cardoso, Gabriel Lopes
Nampuri, Suresh
Rosselló, Martí
Source :
Annales Henri Poincaré. Sep2024, Vol. 25 Issue 9, p4065-4120. 56p.
Publication Year :
2024

Abstract

The 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 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 / Φ 10 . The construction uses two distinct SL (2 , Z) subgroups of 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 / η 24 by means of a continued fraction structure. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
14240637
Volume :
25
Issue :
9
Database :
Academic Search Index
Journal :
Annales Henri Poincaré
Publication Type :
Academic Journal
Accession number :
179167656
Full Text :
https://doi.org/10.1007/s00023-023-01400-3