# Proving conformal invariance of a field theory by property of its stress energy tensor.

I have a question about proving conformal invariance of a field theory by property of its stress energy tensor.

In physics there is argument that when the stress-energy tensor is traceless, symmetry, holomorphic, the QFT is conformal invariance.

But is there a rigorous math proof of this?

• What kind of formalization of field theory did you have in mind?
– j.c.
Oct 4, 2013 at 15:11
• In the sense of constructive QFT, namely the probability framework. Oct 9, 2013 at 5:14
• This is probably not a necessary criterion, because by taking countably many massless free fields, you get a conformal QFT which is even globally conformal invariant but has no stress energy tensor ("the central charge is infinity"). About how many dimensions are you talking, maybe I can cook you up an argument, when this is sufficient. Dec 9, 2013 at 9:10
• Thanks, I am thinking about the CFT that appears in 2-d stat physics, and mostly c<=1. Dec 11, 2013 at 0:41
• For example, for a boundary QFT defined on a simply connected bounded domain, we should be an equivalent condition for the QFT to be conformal invariance.(Say, the "measure" is invariant under the conformal transformation from the domain to disk. Or for the correlation function to be covariant.) Dec 11, 2013 at 0:46