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We identify the untwisted moduli of heterotic orbifold compactifications forthe case, when the gauge twist is realized by a rotation. The Wilson lines arefound to have both continuous and discrete parts. For the case of the standardZ(3) orbifold we classify all possibilities of breaking the gauge group E(6)times SU(3) by nine of the eighteen Wilson moduli and by additional discreteWilson lines.Comment: 27 pages, LATEX, MS-TPI-93-0

ORBIFOLD COMPACTIFICATIONS WITH CONTINUOUS WILSON LINES