CONSISTENCY OF M-THEORY ON NON-ORIENTABLE MANIFOLDS

We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. Our approach is computational. We determine the generators for the 12-dimensional bordism group of pin manifolds with a w(1)-twisted integer lift of w(4); these are the manifolds on which Wick-rotated M-theory exists. The anomaly cancellation comes down to computing a specific eta-invariant and cubic form on these manifolds. Of interest beyond this specific problem are our expositions of computational techniques for eta-invariants, the algebraic theory of cubic forms, Adams spectral sequence techniques and anomalies for spinor fields and Rarita-Schwinger fields.

Automated summary

The study proves the absence of parity anomaly in M-theory in the low-energy field theory approximation through computational methods. It determines the generators for the 12-dimensional bordism group of pin manifolds with specific characteristics. The study not only solves a specific problem but also demonstrates various computational techniques and algebraic theories.