# About the general expression of trace anomaly and CFT partition functions

Here I am putting up a slightly different version of that question,

• I think the statement is that for any dimensional CFT the following is true,

$$\langle T^{\mu}_\mu \rangle = \sum B_n I_n - 2(-1)^{d/2}AE_d,$$

where $E_d$ is the "Euler density" and $I_n$ are the independent "Weyl invariants of weight $-d$".

(...I am not sure of the definition of the geometric quantities coming on the R.H.S and I wonder if the notion of the "Euler density" and `Weyl invariants" are related to the ideas of the Weyl tensor and the Euler tensor..)

• Also a similar sounding statement that I see is as in equation 15 (page 5) of http://arxiv.org/abs/hep-th/9806087

One can see the stark similarity between that the equation referred to in the linked paper and the statement of trace anomaly that I have typed in the first bullet point.

I can't find a reference to the derivation of these results and/or the relationship between these statements. It would be great if someone can help with this.