Heterotic global anomalies and torsion Witten index

Abstract

We study the structure of anomalies in general heterotic string theories by considering general 2-dimensional $$ \mathcal{N} $$ N = (0, 1) supersymmetric quantum field theories (SQFTs), without assuming conformal invariance nor the correct central charges. First we generalize the precise notion of the B-field introduced by Witten. Then we express the target space anomalies by invariants of SQFTs. Perturbative anomalies correspond to the Witten index of some class of SQFTs, while global anomalies correspond to a torsion version of the Witten index. The torsion index gives some of the invariants of SQFTs suggested by topological modular forms, and is expected to be zero for the cases that are relevant to actual heterotic string theories.

A Panorama Of Physical Mathematics c. 2022

“…The Stolz-Teichner program grew out of attempts to extend the ideas of Graeme Segal on elliptic cohomology to a theory conjecturally equivalent to the theory of topological modular forms. The subject has recently gotten a big boost from several recent works applying it to interesting questions in quantum field theory [222][223][224] and anomaly cancellation in heterotic string theory [225][226][227]. There is clearly a lot more to be learned in this subject.…”

“…For example, this is fairly nontrivial in compactifications of F-theory to 6d [447][448][449][450][451][452]. Some recent very intriguing work on anomaly cancellation in heterotic string theory can be found in [225][226][227]. These latter papers are particularly notable for their heavy use of the Stolz-Teichner conjecture relating the topology of the space of (0,1) supersymmetric 2d QFTs to topological modular forms.…”