Gravitational Couplings and $Z_2$ Orientifolds

Abstract

The interplay between gravitational couplings on branes and the occurrence of fractional flux in low dimensional orientifolds is examined. It is argued that gravitational couplings need to be assigned not only to D-branes but also to orientifold planes. The fractional charges of the orientifold $d$-planes can be understood in terms of flux quantization of the $d-3$ form potential and modified Bianchi identities. Detailed results are presented for the case of the type IIB orientifold on $T^6/Z_2$, which is dual to F-theory on a complex 4-fold with terminal singularities.

24 pages, harvmac,Numerical coefficients of R^4 couplings have been corrected, and are now in agreement with recent results of hep-th/9812071 and hep-th/9812088. No other changes. This revision supercedes the published version of this paper

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