A Is There a Spectral-Flow Explanation for Bosonic Self-Dual Tensor Anomalies?

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William Nelso
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I like the spectral-flow viewpoint on chiral anomalies, as described for instance in Peskin & Schroeder, last part of Ch. 19.1 This appears to depend crucially on the concept of fermi sea level, making it specific to fermions. However, bosonic self-dual tensor fields also have an anomaly (gravitational). Hence my question - is there a similar understanding for this type of anomaly? I have not been able to find this question addressed.
 
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Where in this section precisely do you see anything about the Fermi sea? The book is not about many-body physics!
 

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