The exact 8d chiral ring from 4d recursion relations

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 tau(z) is identified with the low-energy effective coupling of the four-dimensional N=2 super Yang-Mills theory with gauge group SU(2) and Nf=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 tau profile. Here we apply to the SU(2), Nf=4 theory some recursion techniques that allow to derive the coefficients of the large-z expansion of tau in terms of modular functions of the UV coupling. 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.

23 pages, Latex2e

References in corpus (7)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Particle Physics Implications of F-theory
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Exotic instanton counting and heterotic/type I' duality
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• Exotic prepotentials from D(-1)D7 dynamics
• Holographic non-perturbative corrections to gauge couplings

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• Modular Anomaly from Holomorphic Anomaly in Mass Deformed N=2 Superconformal Field Theories
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Non-perturbative studies of N=2 conformal quiver gauge theories
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• Non-perturbative gauge couplings from holography