Saturday 11 April 2020

quantum field theory - can gapped systems have gravitational anomalies?



The question is in the title.


If it is possible, what are some examples of gapped systems--either quantum field theories or condensed matter systems--which exhibit some kind of anomaly when coupled to a metric with curvature or placed on a spacetime with non-trivial topology?



Answer



The answer to my question is Yes.


Embarrassingly, one of the simplest examples is given by the fermionic quasistring topological order I described in my paper http://arxiv.org/abs/1404.4385 . The magic is that the 5th oriented bordism group is generated by the mapping torus of complex conjugation on CP^2. Thus, if we consider the fermionic quasistring top order on CP^2, the action changes by a sign when we perform the large diffeomorphism of complex conjugation on CP^2.


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