Anomalous U(1)'s in Type I and Type IIB D = 4, N = 1 string vacua

Ws study the cancellation of U(1) anomalies in Type I and Type IIB D = 4, N = 1 string vacua. We first consider the case of compact toroidal Z(N) Type IIB orientifolds and then proceed to the non-compact case of Type IIB D3-b ranes at orbifold and orientifold singularities. Unlike the case of the het erotic string we find that for each given vacuum one has generically more t han one U(1) with non-vanishing triangle anomalies. There is a generalized Green-Schwarz. mechanism by which these anomalies are cancelled. This invol ves only the Ramond-Ramond scalars coming from the twisted closed string sp ectrum but not those coming from the untwisted sector. Associated to the an omalous U(1)'s there are field-dependent Fayet-Iliopoulos terms whose mass scale is fixed by undetermined vev's of the NS-NS partners of the relevant twisted RR fields. Thus. unlike what happens in heterotic vacua, the masses of the anomalous U(1)'s gauge bosons may be arbitrarily tight. In the case of D3-branes at singularities, appropriate factorization of the U(1)'s con strains the Chan-Paton matrices beyond the restrictions from cancellation o f nonabelian anomalies. These conditions can be translated to constraints o n the T-dual Type IIB brane box configurations. We also construct a new lar ge family of N = 1 chiral gauge field theories from D3-branes at orientifol d singularities, and check its non-abelian and U(1) anomalies cancel. (C) 1 999 Elsevier Science B.V.