Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory

Details Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory

2002-06-21

arxiv.org/abs/hep-th/0206203v2

JHEP 0207 (2002) 066

Physics

High Energy Physics

High Energy Physics - Theory

81 pages, LaTeX, corrected typos

Scientific paper

10.1088/1126-6708/2002/07/066

The non-perturbative superpotential generated by a heterotic superstring wrapped once around a genus-zero holomorphic curve is proportional to the Pfaffian involving the determinant of a Dirac operator on this curve. We show that the space of zero modes of this Dirac operator is the kernel of a linear mapping that is dependent on the associated vector bundle moduli. By explicitly computing the determinant of this map, one can deduce whether or not the dimension of the space of zero modes vanishes. It is shown that this information is sufficient to completely determine the Pfaffian and, hence, the non-perturbative superpotential as explicit holomorphic functions of the vector bundle moduli. This method is illustrated by a number of non-trivial examples.

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