Threshold corrections, generalised prepotentials and Eichler integrals

Carlo Angelantonj (1) , Ioannis Florakis (2) , Boris Pioline (3, 4, 5)

1 dipartimento di fisica teorica
2 CERN [Genève]
3 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
4 SU - Sorbonne Université
5 UPMC - Université Pierre et Marie Curie - Paris 6

We continue our study of one-loop integrals associated to BPS-saturated amplitudes in $\mathcal{N}=2$ 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-Poincar\'e series in the complex structure modulus. The closure of Niebur-Poincar\'e series under modular derivatives implies that such integrals derive from holomorphic prepotentials $f_n$, generalising the familiar prepotential of $\mathcal{N}=2$ 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 ${\varGamma}_0(N)$ Hauptmodul, a full characterisation of holomorphic prepotentials including their quantum monodromies, as well as concrete formulae for holomorphic Yukawa couplings.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Carlo Angelantonj, Ioannis Florakis, Boris Pioline. Threshold corrections, generalised prepotentials and Eichler integrals. Nuclear Physics B, 2015, 897, pp.781-820. ⟨10.1016/j.nuclphysb.2015.06.009⟩. ⟨hal-01113281⟩