Anomaly cancellation in M-theory on orbifolds

TL;DR

This paper calculates anomaly cancellation in M-theory on orbifolds using the upstairs approach, demonstrating the equivalence with the downstairs approach and constructing explicit anomaly-free solutions including five-branes.

Contribution

It provides a detailed method for anomaly cancellation in M-theory orbifolds using the upstairs approach, including solutions with five-branes and showing equivalence with the downstairs approach.

Findings

Explicit anomaly-free solutions for $S^1/Z_2$ and $T^5/Z_2$ orbifolds.

Demonstration of equivalence between upstairs and downstairs approaches.

Consistent anomaly cancellation with five-branes included.

Abstract

We present calculation of the anomaly cancellation in M-theory on orbifolds $S^1/Z_2$ and $T^5/Z_2$ in the upstairs approach. The main requirement that allows one to uniquely define solutions to the modified Bianchi identities in this case is that the field strength $G$ be globally defined on $S^1$ or $T^5$ and properly transforming under $Z_2$. We solve for general $G$ that satisfies these requirements and explicitly construct anomaly-free theories in the upstairs approach. We also obtain the solutions in the presence of five-branes. All these constructions show equivalence of the downstairs and upstairs approaches. For example in the $S^1/Z_2$ case the ten-dimensional gauge coupling and the anomaly cancellation at each wall are the same as in the downstairs approach.