Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds

Details Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds

1996-04-17

arxiv.org/abs/hep-th/9604097v3

Nucl.Phys. B474 (1996) 323-342

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, LaTex. final version, to appear in Nucl. Phys. B

Scientific paper

10.1016/0550-3213(96)00268-4

We elucidate the interplay between gauge and supersymmetry anomalies in six-dimensional $N=1$ supergravity with generalized couplings between tensor and vector multiplets. We derive the structure of the five-dimensional supergravity resulting from the $S_1$ reduction of these models and give the constraints on Chern-Simons couplings that follow from duality to $M$ theory compactified on a Calabi-Yau threefold. The duality is supported only on a restricted class of Calabi-Yau threefolds and requires a special type of intersection form. We derive five-dimensional central-charge formulas and discuss briefly the associated phase transitions. Finally, we exhibit connections with $F$-theory compactifications on Calabi-Yau manifolds that admit elliptic fibrations. This analysis suggests that $F$ theory unifies Type-$IIb$ three-branes and $M$-theory five-branes.

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