A Non-Perturbative Superpotential With $E_8$ Symmetry

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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Additional references and clarifications. Latex, 10 pages

Scientific paper

10.1142/S0217732396002198

We compute the non-perturbative superpotential in $F$-theory compactification
to four dimensions on a complex three-fold $\P^1\times S$, where $S$ is a
rational elliptic surface. In contrast to examples considered previously, the
superpotential in this case has interesting modular properties; it is
essentially an $E_8$ theta function.

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