1997/10/17 by J. A. Minahan, J.A. Minahan, D. Nemeschansky +2 · 5 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1016/s0550-3213(98)00314-9
published as Nucl.Phys. B528 (1998) 109-132 · harvmac(b) 28 pages
arxiv created 1997/10/17 · openalex publication_date 1998/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We derive modular anomaly equations from the Seiberg-Witten-Donagi curves for softly broken N=4 SU(n) gauge theories. From these equations we can derive recursion relations for the pre-potential in powers of m2, where m is the mass of the adjoint hypermultiplet. Given the perturbative contribution of the pre-potential and the presence of ``gaps'' we can easily generate the m2 expansion in terms of polynomials of Eisenstein series, at least for relatively low rank groups. This enables us to determine efficiently the instanton expansion up to fairly high order for these gauge groups, e. g. eighth order for SU(3). We find that after taking a derivative, the instanton expansion of the pre-potential has integer coefficients. We also postulate the form of the modular anomaly equations, the recursion relations and the form of the instanton expansions for the SO(2n) and En gauge groups, even though the corresponding Seiberg-Witten-Donagi curves are unknown at this time.