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We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter.
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J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string · 2007
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J. Bruning and M. Lesch, On the eta invariant of certain nonlocal boundary value problems
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