Localization of heterotic anomalies on various hypersurfaces ofT6/Z4

Abstract

We investigate the structure of local anomalies of heterotic E 8 × E 8 ′ theory on T 6 /Z 4 . We show that the untwisted states lead to anomalies in ten, six and four dimensions. At each of the six dimensional fixed spaces of this orbifold the twisted states ensure, that the anomalies factorize separately. As some of these twisted states live on T 2 /Z 2 , they give rise to four dimensional anomalies as well. At all four dimensional fixed points at worst a single Abelian anomaly can arise. Since the anomalies in all these dimensions factorize in a universal way, they can be canceled simultaneously. In addition, we show that for all U(1) factors at the four dimensional fixed points at least logarithmically divergent Fayet-Ilopoulos tadpoles are generated.

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

“…Let us now determine the four dimensional mass spectrum of the anomalous U(1) A photon field together with the Green-Schwarz vector or tensor fields. At first sight it seems that the two formulations lead to very different mass spectra, since in the vector formulation (21) there are divergent boundary mass terms which are absent in the dual tensor formulation (22). This would then contradict the equivalence of the two dual formulations.…”

GaugedD=7supergravity on theS1/Z2orbifold

“…This should not be anticipated for the brane worlds constructed in five dimensions [8], [9], where the boundary gauge group is not restricted by any local anomaly, although global anomalies may impose some constraints [10,11,12]. However, gravitational anomalies also exist in six dimensions [13], and this places nontrivial constraints on six-dimensional (6D) theories [14]- [21]. Therefore, it is expected that the matter on six-dimensional brane worlds in seven dimensions will also be restricted, and may even be uniquely specified, by anomaly cancellation.…”

“…We should here remark that the action of the theory may in principle include the topological mass term 21) which is present in the pure supergravity case (no vector multiplets). This term has important implications for the 6-dimensional theory obtained by reduction on S 1 [33] while, in the context of S 1 /Z 2 compactification, its variation contributes to the anomaly and the anomaly cancellation conditions lead to a relation fixing the boundary Yang-Mills coupling in terms of the gravitational coupling and h [18,19].…”

“…(5.19) and (5.20) are similar to the conditions found in [49] and they are interpreted as follows. The first two conditions of (5.19) can be used to determine c z andc z : real solutions exist when β 21) in which case they are given by the roots of the equation…”

A Z2×Z2 standard model

“…they are Wilson lines on the underlying torus but not on the orbifold (see e.g. [10,31]). By contrast, W is a Wilson line also on the orbifold.…”