Anomaly cancellation by generalised cohomology

TL;DR

This paper explores how generalized cohomology theories can unify perturbative and non-perturbative aspects of string theory, providing insights into anomaly cancellation and the topological nature of supersymmetry.

Contribution

It introduces a novel application of universal coefficient theorems in linking different cohomology theories to string theory domains and anomaly cancellation.

Findings

Universal coefficient theorem connects cohomology theories with different topological features.

Topological features influence the detection of supersymmetry by observers.

Framework links perturbative and non-perturbative string theory sectors.

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 ref. [11]. 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.