Abstract
We study the possibility that the ten-dimensional (D=10) heterotic superstring generates a class of Chern-Simons theories in three dimensions, via compactifications on the internal seven-dimensional manifolds. We give an explicit example of such compactifications on (Calabi-Yau)6×S1×(Mink.)3, using the dual formulation of the heterotic string. The string tension 1/α′ as well as the Yang-Mills coupling constant g2 in D=10 is double-quantized in terms of two integers, through a condensate of the antisymmetric field strength NM1…M7, which is dual to the ordinary field strength GMNP. The resultant Chern-Simons theory has the gauge group E6⊗E8, containing also the usual kinetic terms of the gauge fields, which may be interpreted as regulator terms. This result suggests a close relationship between the D=10 heterotic string and D=3 Chern-Simons theory.
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