I am reading the chapters on characteristic classes and the index theorems in Nakahara. It is proven in the text that any chiral or gravitational anomaly A is given by
A=∫I12r
with I12r given by the descent equation,
I2r+2=dI2r+1
δgaugeI2r+1=dI12r
The various I's are related to the theory of the characteristic classes and Chern-Simons forms. On the other hand, the trace anomaly cannot be written in this way, at least I cannot see how. In 2 and 4 dimension we have (see for instance Duff),
(T2)μμ=cR
(T4)μμ=cW2+aE4+fFμνFμν
where W2 is the Weyl tensor squared and E4=R2μνρσ−4R2μν+R2 (with some numerical coefficient) is the Euler density. This got me thinking: is there a geometric way to describe the anomaly, i.e. to write a descent equation and the index theorem for those anomalies?
Any pointers to papers, lecture notes, books or other resources are most welcome!
This post imported from StackExchange Physics at 2014-06-27 11:32 (UCT), posted by SE-user Bulkilol