Vector bundle moduli, small instanton transitions and nonperturbative superpotentials in heterotic M-theory
Abstract
In this thesis, we give the general prescription for calculating the moduli of irreducible, stable SU (n ) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory. Explicit results are presented for Hirzebruch base surfaces. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. We present a method for explicitly computing the non-perturbative superpotentials associated with the vector bundle moduli in heterotic superstrings and M-theory. The non-perturbative superpotential generated by a heterotic superstring wrapped 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 examples.
Recommended Citation
Evgeny I Buchbinder,
"Vector bundle moduli, small instanton transitions and nonperturbative superpotentials in heterotic M-theory"
(January 1, 2003).
Dissertations available from ProQuest.
Paper AAI3095862.
http://repository.upenn.edu/dissertations/AAI3095862
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