Talk:Non-unitary conformal field theory

Semi-definite programming
Challenge seems to be that we should bound the contributions of infinitely many primary fields with higher conformal dimensions and/or spins, whose signs can be arbitrary. For example, in the 3d Ising model, we assume that we know all operators of dimension 3 or less, and we have to bound the contributions of the rest. There are asymptotic bounds that should also hold in the non-unitary case. Can we find a set of assuptions on non-unitary CFTs that allow us to make progress?

Assumption that three-point structure constants are real, but two-points fct are $$\pm 1$$, might work, especially in the context of multi-correlator bootstrap, since the same field with the same sign appears in various correlators? Maybe not: spectrum can be dense or continuous, fields can have multiplicities; positivity can control any distribution of fields, but without positivity there is apparently no control.

It would be interesting to know how many fields with negative two-point functions there are in non-unitary minimal models. Finitely many would be great. In the Q-Potts model we have infintely many logarithmic fields, but structures of representations are not directly related to signs of two-point functions.

Wish list
We need a method that is able to exclude some regions in parameter space under certain assumptions.

The challenge is to replace the positivity assumptions that hold in unitary CFTs, with mere convergence of conformal block decompositions.