On four-dimensional compactifications of F-theory

Branches of moduli space of F-theory in four dimensions are investigated. The transition between two branches is described as a 3-brane-instanton transition on a 7-brane. A dual heterotic picture of the transition is presented and the F-theory-heterotic theory map is given. The F-theory data, complex structure of the Calabi-Yau fourfold and the instanton bundle on the 7-brane is mapped to the heterotic bundle on the elliptic Calabi-Yau threefold CY3. The full moduli space has a web structure which is also found in the moduli space of semi-stable bundles on CY3. Matter content of the four-dimensional theory is discussed in both F-theory and heterotic theory descriptions. (C) 1997 Elsevier Science B.V.