Tadpole versus anomaly cancellation in D=4,6 compact IIB orientifolds

TL;DR

The paper investigates how tadpole cancellation and gauge anomaly cancellation relate in compact Type IIB orientifolds with D9/D5-branes in D=4, N=1 and comments on the D=6 case. By expressing anomaly conditions through traces of Chan-Paton twist matrices and comparing them to tadpole constraints, the authors show that tadpoles are generally more restrictive than anomaly cancellation in 4D, and that compactness introduces extra tadpole requirements not tied to anomalies. They identify new tadpole solutions for Z_6 and Z_{12} that yield gauge groups not previously reported, and demonstrate that mixed U(1) and gravitational anomalies cancel automatically when non-Abelian anomalies do, via a Green–Schwarz mechanism with twisted RR fields. In D=6 there is a full equivalence between tadpole and anomaly cancellation due to the lack of RR flux escape. These results clarify the limits of inferring gauge content from tadpoles alone and reveal a richer structure for compact models.

Abstract

It is often stated in the literature concerning D=4,6 compact Type IIB orientifolds that tadpole cancellation conditions i) uniquely fix the gauge group (up to Wilson lines and/or moving of branes) and ii) are equivalent to gauge anomaly cancellation. We study the relationship between tadpole and anomaly cancellation conditions and qualify both statements. In general the tadpole cancellation conditions imply gauge anomaly cancellation but are stronger than the latter conditions in D=4, N=1 orientifolds. We also find that tadpole cancellation conditions in Z_N D=4,6 compact orientifolds do not completely fix the gauge group and we provide new solutions different from those previously reported in the literature.