Eigenvalues in xAct

[Kabouter9]

Hi all,

I'm currently trying to reproduce the results from this paper:https://inspirehep.net/literature/2144158. In particular, I'm looking at the equations in Appendix B, and try to put these into a matrix with the use of xAct with the eye on calculating its eigenvalues.

However, doing so leads to some error which I have no idea how to solve.

I'll attach my notebook and a screenshot of my matrix (which may be incorrect as I encounter errors) here.

Any help would be appreciated!

Thanks!

[Jose]

Hi,

This computation is too large for me to absorb and debug, but let me say this: You are calling Eigenvalues on a 10x10 matrix whose entries have free indices. I don't see how this can work. The determinant is not a scalar. Note in particular that a quick check of index characters shows that your entry 13 has indices c, d with wrong sign. It should be

    mat1[[1, 3]] = -2 \[Alpha][] gammabar[-i, -c] gammabar[-j, -d]

The particular error you see seems to be coming from an internal computation of the form Roots[...== 0, ...] where the RHS of the equation is a complicated tensor with 10 free indices. It interferes somehow with xTensor's IsIndexOf (I guess due to finding free indices where they are not expected). Try deactivating the latter with

   Block[{IsIndexOf}, Eigenvalues[mat1]]

But still this seem too complicated and it didn't finish for me in a minute or so I waited... Sorry, I cannot help more.

Cheers,

Jose.