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I attempt to analyse the next-to-leading-order non-holomorphic contributionto the Wilsonian low-energy effective action in the four-dimensional N=2 gaugetheories with matter, from the manifestly N=2 supersymmeric point of view, byusing the harmonic superspace. The perturbative one-loop correction is found tobe in agreement with the N=1 superfield calculations of de Wit, Grisaru andRocek. The previously unknown coefficient in front of this non-holomorphiccorrection is calculated. A special attention is devoted to the N=2superconformal gauge theories, whose one-loop non-holomorphic contribution islikely to be exact, even non-perturbatively. This leading (one-loop)non-holomorphic contribution to the LEEA of the N=2 superconformally invariantgauge field theories is calculated, and it does not vanish, similarly to thecase of the N=4 super-Yang-Mills theory.Comment: 15 pages, LaTeX; changes in the abstract and in sect.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Next-to-leading-order correction to the effective action in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>gauge theories

Next-to-leading-order correction to the effective action inN=2gauge theories