Heterotic Anomaly Cancellation in Five Dimensions

We study the constraints on five-dimensional N=1 heterotic M-theory imposed by a consistent anomaly-free coupling of bulk and boundary theory. This requires analyzing the cancellation of triangle gauge anomalies on the four-dimensional orbifold planes due to anomaly inflow from the bulk. We find that the semi-simple part of the orbifold gauge groups and certain U(1) symmetries have to be free of quantum anomalies. In addition there can be several anomalous U(1) symmetries on each orbifold plane whose anomalies are cancelled by a non-trivial variation of the bulk vector fields. The mixed U(1) non-abelian anomaly is universal and there is at most one U(1) symmetry with such an anomaly on each plane. In an alternative approach, we also analyze the coupling of five-dimensional gauged supergravity to orbifold gauge theories. We find a somewhat generalized structure of anomaly cancellation in this case which allows, for example, non-universal mixed U(1) gauge anomalies. Anomaly cancellation from the perspective of four-dimensional N=1 effective actions obtained from E_8xE_8 heterotic string- or M-theory by reduction on a Calabi-Yau three-fold is studied as well. The results are consistent with the ones found for five-dimensional heterotic M-theory. Finally, we consider some related issues of phenomenological interest such as model building with anomalous U(1) symmetries, Fayet-Illiopoulos terms and threshold corrections to gauge kinetic functions.Comment: 46 pages, Late

Computation of generalized equivariant cohomologies of Kac-Moody flag varieties

In 1998, Goresky, Kottwitz, and MacPherson showed that for certain projective varieties X equipped with an algebraic action of a complex torus T, the equivariant cohomology ring H_T(X) can be described by combinatorial data obtained from its orbit decomposition. In this paper, we generalize their theorem in three different ways. First, our group G need not be a torus. Second, our space X is an equivariant stratified space, along with some additional hypotheses on the attaching maps. Third, and most important, we allow for generalized equivariant cohomology theories E_G^* instead of H_T^*. For these spaces, we give a combinatorial description of E_G(X) as a subring of \prod E_G(F_i), where the F_i are certain invariant subspaces of X. Our main examples are the flag varieties G/P of Kac-Moody groups G, with the action of the torus of G. In this context, the F_i are the T-fixed points and E_G^* is a T-equivariant complex oriented cohomology theory, such as H_T^*, K_T^* or MU_T^*. We detail several explicit examples.Comment: 19 pages, 6 figures, this is a new and completely modified version of DG/040207

Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds

We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in [arXiv:1303.1832]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html .Comment: 25 pages, 7 figures, 1 table. v2: references added and minor changes. Final version accepted for publicatio