Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-09-06
Nucl.Phys. B513 (1998) 405-444
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, Tex, no figures
Scientific paper
10.1016/S0550-3213(97)00763-3
The Seiberg-Witten curve and differential for ${\cal N}=2$ supersymmetric SU(N) gauge theory, with a massive hypermultiplet in the adjoint representation of the gauge group, are analyzed in terms of the elliptic Calogero-Moser integrable system. A new parametrization for the Calogero-Moser spectral curves is found, which exhibits the classical vacuum expectation values of the scalar field of the gauge multiplet. The one-loop perturbative correction to the effective prepotential is evaluated explicitly, and found to agree with quantum field theory predictions. A renormalization group equation for the variation with respect to the coupling is derived for the effective prepotential, and may be evaluated in a weak coupling series using residue methods only. This gives a simple and efficient algorithm for the instanton corrections to the effective prepotential to any order. The 1- and 2- instanton corrections are derived explicitly. Finally, it is shown that certain decoupling limits yield ${\cal N}=2$ supersymmetric theories for simple gauge groups $SU(N_1)$ with hypermultiplets in the fundamental representation, while others yield theories for product gauge groups $SU(N_1) \times ...\times SU(N_p)$, with hypermultiplets in fundamental and bi-fundamental representations. The spectral curves obtained this way for these models agree with the ones proposed by Witten using D-branes and M-theory.
D'Hoker Eric
Phong Duong Hong
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