Localized tadpoles of anomalous heterotic U(1)'s

Abstract

We investigate the properties of localized anomalous U(1)'s in heterotic string theory on the orbifold T 6 /Z 3 . We argue that the local four dimensional and original ten dimensional Green-Schwarz mechanisms can be implemented simultaneously, making the theory manifestly gauge invariant everywhere, in the bulk and at the fixed points. We compute the shape of the Fayet-Iliopoulos tadpoles, and cross check this derivation for the four dimensional auxiliary fields by a direct calculation of the tadpoles of the internal gauge fields. Finally we study some resulting consequences for spontaneous symmetry breaking, and derive the profile of the internal gauge field background over the orbifold.

Higher derivative operators from Scherk-Schwarz supersymmetry breaking on Script T2/Z2.

“…On the other hand, in SO(10) case [23], one has massless Q and L in (4,2,1) under the Pati-Salam group from two bulk 16's. In this case, there would appear the localised anomalies with split multiplets which should be cancelled by a localised Green-Schwarz mechanism [24].…”

Vector-tensor duality in the five dimensional supersymmetric Green-Schwarz mechanism

“…In this case one similarly finds that the two-form description is free of singular terms, while in the dual formulation involving a six-form the singular δ(0) term arises as well, as can be inferred from ref. [21]. Furthermore, by introducing the gauge invariant three-form field strength H = dB 2 +ω 3 (A) one obtains the anomalous Bianchi identity d H = F 2 2 .…”

Higgs-gauge unification without tadpoles

“…In this way the tadpole quadratic divergence amounts to a quadratic divergence for the Higgs-gauge field squared mass and spoils the little hierarchy we wanted to solve. The existence of such tadpoles is a generic feature of orbifold compactifications in dimensions D ≥ 6 and has been confirmed in six-dimensional orbifold field [12] and ten-dimensional string [19] theories. One way out [12] is that local tadpoles vanish globally and thus they would not spoil the four dimensional effective theory, although this requires a strong restriction on the bulk fermion content.…”