Anomalies of E8 gauge theory on String manifolds

Abstract

In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory partition function of Diaconescu-Moore-Witten extends from the Spin case to the String case. Third, that the cubic refinement law of Diaconescu-Freed-Moore for the phase of the M-theory partition function extends to String manifolds. The analysis relies on extending from invariants which depend on the Spin structure to invariants which instead depend on the String structure. Along the way, the one-loop term is refined via the Witten genus.

19 pages, expanded, a whole new section added on the refined invariants related to String structure

References in corpus (5)

• One loop in eleven dimensions
• D-instantons, Strings and M-theory
• A Note on Low-Dimensional String Compactifications
• Type IIB String Theory, S-Duality, and Generalized Cohomology
• On effective F-theory action in type IIA compactifications

Cited by in corpus (9)

• The anomaly that was not meant IIB
• Framed M-branes, corners, and topological invariants
• The E8 moduli 3-stack of the C-field in M-theory
• Geometry of Spin and Spin^c structures in the M-theory partition function
• The character map in (twisted differential) non-abelian cohomology
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• M-theory, the signature theorem, and geometric invariants
• Variations of rational higher tangential structures
• Topological actions via gauge variations of higher structures