# Can gapped systems have gravitational anomalies?

+ 5 like - 0 dislike
259 views

I'm interested in gravitational anomalies both which arise when coupling to curvature fluctuations or when placing the system on a manifold of non-trivial topology.

Intuitively, we can compare the curvature radius to 1/gap if we have some characteristic velocity. However, an anomaly is some discrete behavior, so even if the curvature radius is much larger than 1/gap, the effect may be hard to measure but it could still be there, so this does not rule out a gravitational anomaly of the first kind.

asked Jun 26, 2014
edited Jun 26, 2014

## 1 Answer

+ 4 like - 0 dislike

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.

answered Sep 6, 2014 by (1,925 points)

## Your answer

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOver$\varnothing$lowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.