Journal of High Energy Physics

, 2011:77 | Cite as

The exact 8d chiral ring from 4d recursion relations

  • M. Billò
  • M. Frau
  • L. Gallot
  • A. Lerda
Open Access


We consider the local F-theory set-up corresponding to four D7 branes in type I′ theory, in which the exact axio-dilaton background τ(z) is identified with the low-energy effective coupling of the four-dimensional \( \mathcal{N} = 2 \) super Yang-Mills theory with gauge group SU(2) and N f  = 4 flavours living on a probe D3 brane placed at position z. Recently, an intriguing relation has been found between the correlators forming the chiral ring of the eight-dimensional theory on the D7 branes and the large-z expansion of the τ profile. Here we apply to the SU(2) N f  = 4 theory some recursion techniques that allow to derive the coefficients of the large-z expansion of τ in terms of modular functions of the UV coupling τ 0. In this way we obtain exact expressions for the elements of the eight-dimensional chiral ring that resum their instanton expansions, previously known only up to the first few orders by means of localization techniques.


D-branes F-Theory Supersymmetric Effective Theories 


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© The Author(s) 2011

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Authors and Affiliations

  1. 1.Dipartimento di Fisica Teorica, Università di Torino, and I.N.F.N. — Sezione di TorinoTorinoItaly
  2. 2.LAPTH, Université de Savoie, CNRSAnnecy le Vieux CedexFrance
  3. 3.Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale, and I.N.F.N. — Gruppo Collegato di Alessandria — Sezione di TorinoAlessandriaItaly

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