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We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is classified by cohomology and how extending the orbifold group can remove it. Working with such extensions requires an understanding of the consistent ways in which extending groups can act on the twisted states of the original symmetry, which leads us to a discrete-torsion like choice that exists in orbifolds with trivially-acting subgroups. We review a general method for constructing such extensions and investigate its application to orbifolds. Through numerous explicit examples we test the conjecture that consistent extensions should be equivalent to (in general multiple copies of) orbifolds by non-anomalous subgroups.
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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.
We show that the number of half-supersymmetric p-branes in the Type II theories compactified on orbifolds is determined by the wrapping rules recently introduced, provided that one accounts correctly for both geometric and non-geometric T-dual configurations. Starting from the Type II theories compactified on K3, we analyze their toroidal dimensional reductions, showing how the resulting half-supersymmetric p-branes satisfy the wrapping rules only by taking into account all the possible higher-dimensional origins. We then consider Type II theories compactified on the orbifold T^6/(Z_2 times Z_2 ), whose massless four-dimensional theory is an N=2 supergravity. Again, the wrapping rules are obeyed only if one includes the complete orbit of the T-duality group, namely either Type IIA or Type IIB theories compactified on either the geometric or the non-geometric T-dual orbifold. Finally, we comment on the interpretation of our results in the framework of the duality between the Heterotic string compactified on K3 times T^2 and the Type II string compactified on a Calabi-Yau threefold.
We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.
We revisit quantum field theory anomalies, emphasizing the interplay with diffeomorphisms and supersymmetry. The Ward identities of the latter induce Noether currents of all continuous symmetries, and we point out how these consistent currents are replaced by their covariant form through the appearance of the Bardeen-Zumino currents, which play a central role in our study. For supersymmetry Ward identities, two systematic methods for solving the Wess-Zumino consistency conditions are discussed: anomaly inflow and anomaly descent. The simplest inflows are from supersymmetric Chern-Simons actions in one dimension higher, which are used to supersymmetrize flavor anomalies in $d=4$ and, for $d=2$ $mathcal{N}=(p,q)$, flavor anomalies with $p,qleq 3$ and Lorentz-Weyl anomalies with $p,qleq 6$. Finally, we extend the BRST algebra and the subsequent descent, a necessity for the diffeomorphism anomaly in retrospect. The same modification computes the supersymmetrized anomalies, and determines the above Chern-Simons actions when these exist.
Anomalies in Yang-Mills type gauge theories of gravity are reviewed. Particular attention is paid to the relation between the Dirac spin, the axial current j_5 and the non-covariant gauge spin C. Using diagrammatic techniques, we show that only generalizations of the U(1)- Pontrjagin four--form F^ F= dC arise in the chiral anomaly, even when coupled to gravity. Implications for Ashtekars canonical approach to quantum gravity are discussed.
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