Anomaly cancellation by generalised cohomology

Abstract

Supersymmetric states in M-theory are mapped after compactification to perturbatively non-supersymmetric states in type IIA string theory, with the supersymmetric parts being encoded in the non-perturbative section of the string theory. An observer unable to recognise certain topological features of string theory will not detect supersymmetry. Such relativity of symmetry can also be derived in the context of Theorem 3 in Patrascu (Phys Rev D 90:045018, 2014). The tool of choice in this context is the universal coefficient theorem linking cohomology theories with coefficients that reveal respectively hide certain topological features. As a consequence of these observations, it is shown that the same theorem is capable of linking perturbative with non-perturbative string theoretical domains. A discussion of inflow anomaly cancellation is also included in the context of universal coefficient theorems.