Skip to Main content Skip to Navigation
Journal articles

A Farey tale for N=4 dyons

Abstract : We study exponentially suppressed contributions to the degeneracies of extremal black holes. Within Sen's quantum entropy function framework and focusing on extremal black holes with an intermediate AdS3 region, we identify an infinite family of semi-classical AdS2 geometries which can contribute effects of order exp(S_0/c), where S_0 is the Bekenstein-Hawking-Wald entropy and c is an integer greater than one. These solutions lift to the extremal limit of the SL(2,Z) family of BTZ black holes familiar from the "black hole Farey tail". We test this understanding in N=4 string vacua, where exact dyon degeneracies are known to be given by Fourier coefficients of Siegel modular forms. We relate the sum over poles in the Siegel upper half plane to the Farey tail expansion, and derive a "Farey tale" expansion for the dyon partition function. Mathematically, this provides a (formal) lift from Hilbert modular forms to Siegel modular forms with a pole at the diagonal divisor.
Document type :
Journal articles
Complete list of metadata
Contributor : Boris Pioline Connect in order to contact the contributor
Submitted on : Monday, May 4, 2009 - 9:01:36 AM
Last modification on : Tuesday, November 16, 2021 - 4:54:24 AM

Links full text


  • HAL Id : hal-00380605, version 1
  • ARXIV : 0904.4253


Sameer Murthy, Boris Pioline. A Farey tale for N=4 dyons. Journal of High Energy Physics, Springer, 2009, pp.JHEP09(2009)022. ⟨hal-00380605⟩



Les métriques sont temporairement indisponibles