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There exist extremal p-brane solutions of $D\!=\!11$ supergravity forp=2~and~5. In this paper we investigate the zero modes of the membrane and thefive-brane solutions as a first step toward understanding the full quantumtheory of these objects. It is found that both solutions possess the correctnumber of normalizable zero modes dictated by supersymmetry.Comment: Minor typos corrected, one reference added, agrees with published  version. 9 RevTeX pages, 1 figure include

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

Zero modes 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>11</mml:mn><mml:mn /></mml:math>membrane and five-brane

Zero modes for theD=11membrane and five-brane