Localized anomalies in heterotic orbifolds

Abstract

Recently spatially localized anomalies have been considered in higher dimensional field theories. The question of the quantum consistency and stability of these theories needs further discussion. Here we would like to investigate what string theory might teach us about theories with localized anomalies. We consider the Z_3 orbifold of the heterotic E_8 x E_8 theory, and compute the anomaly of the gaugino in the presence of Wilson lines. We find an anomaly localized at the fixed points, which depends crucially on the local untwisted spectra at those points. We show that non-Abelian anomalies cancel locally at the fixed points for all Z_3 models with or without additional Wilson lines. At various fixed points different anomalous U(1)s may be present, but at most one at a given fixed point. It is in general not possible to construct one generator which is the sole source of the anomalous U(1)s at the various fixed points.Comment: 31 pages, LaTeX, with figures, v3: corrections to appendix C added, minor changes in the main tex

Localized tadpoles of anomalous heterotic U(1)'s

“…From the four dimensional point of view at fixed point Z s the states A Rs i can be interpreted as scalar matter fields in the representation (3 H , R s ). The representation 3 H is with respect to the holonomy group SU(3) H ⊂ SO(6) ⊂ SO (1,9). (To be precise, the holonomy group of the blow up, the holonomy of the orbifold is Z 3 .)…”

“…In a previous publication [1] we have computed the local anomalies at the fixed points of the orbifold T 6 /Z 3 . We found that the anomaly at fixed point Z s was fully determined by the local spectrum at this fixed point (given by (3) and (20)), and hence ultimately by its local shift vector v s .…”

“…In addition, from the fixed point model analysis it followed, that there are only two types of anomalous U(1)'s at a given fixed point [1]. The relevant E 8 branching rules [39] are given by…”

“…The present paper is the follow up investigation of our recent work [1] on localized anomalies in heterotic orbifold models. Let us therefore briefly summarize the general context and the main findings of that article.…”

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].…”