Abstract
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.
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ArXiv ePrint: 1107.3691
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Billò, M., Frau, M., Gallot, L. et al. The exact 8d chiral ring from 4d recursion relations. J. High Energ. Phys. 2011, 77 (2011). https://doi.org/10.1007/JHEP11(2011)077
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DOI: https://doi.org/10.1007/JHEP11(2011)077