2015/02/28 by Carlo Angelantonj, Ioannis Florakis, Boris Pioline · 23 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Duality (order theory) #Fourier series #Geometry and complex manifolds #Holomorphic function #Mathematical analysis #Mathematical physics #Mathematics #Modular form #Physics #Pure mathematics #Series (stratigraphy) #Supergravity #Supersymmetry #hep-th #math.NT
paper · pdf · doi:10.1016/j.nuclphysb.2015.06.009
published in Nuclear Physics B 897, 781-820 (Elsevier BV) · 46 pages, eqs 4.38, 4.40-4.43 and 4.47 corrected
openalex publication_date 2015/06/14 · arxiv created 2015/06/26 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We continue our study of one-loop integrals associated to BPS-saturated amplitudes in N=2 heterotic vacua. We compute their large-volume behaviour, and express them as Fourier series in the complexified volume, with Fourier coefficients given in terms of Niebur–Poincaré series in the complex structure modulus. The closure of Niebur–Poincaré series under modular derivatives implies that such integrals derive from holomorphic prepotentials fn, generalising the familiar prepotential of N=2 supergravity. These holomorphic prepotentials transform anomalously under T-duality, in a way characteristic of Eichler integrals. We use this observation to compute their quantum monodromies under the duality group. We extend the analysis to modular integrals with respect to Hecke congruence subgroups, which naturally arise in compactifications on non-factorisable tori and freely-acting orbifolds. In this case, we derive new explicit results including closed-form expressions for integrals involving the Γ0(N) Hauptmodul, a full characterisation of holomorphic prepotentials including their quantum monodromies, as well as concrete formulæ for holomorphic Yukawa couplings.