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Exact and microscopic one-instanton calculations in \(N=2\) supersymmetric Yang-Mills theories. (English) Zbl 0925.81371

Summary: We study the low-energy effective theory in \(N=2\) super Yang-Mills theories by microscopic and exact approaches. We calculate the one-instanton correction to the prepotential for any simple Lie group from the microscopic approach. We also study the Picard-Fuchs equations and their solutions in the semi-classical regime for classical gauge groups with rank \(r\leqslant 3\). We find that for gauge groups \(G=A_r, B_r, C_r\;(r\leqslant 3)\) the microscopic results agree with those from the exact solutions.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
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