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Sigma models describing low energy effective actions on D0-brane probes withN=8 supercharges are studied in detail using a manifestly d=1, N=4 super-spaceformalism. Two 0+1 dimensional N=4 multiplets together with their generalactions are constructed. We derive the condition for these actions to be N=8supersymmetric and apply these techniques to various D-brane configurations. Wefind that if in addition to N=8 supersymmetry the action must also have Spin(5)invariance, the form of the sigma model metric is uniquely determined by theone-loop result and is not renormalized perturbatively or non-perturbatively.Comment: Uses harvmac, 16 pages. We correct an error pointed out by E. Witte

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

Nonrenormalization theorem for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn><mml:mn /></mml:math>vector multiplet

Nonrenormalization theorem for thed=1,N=8vector multiplet