Trans-series from condensates

The SVZ sum rules were invented as an analytic approach to non-perturbative
quantum field theory (QFT) and have played a crucial role in QCD phenomenology. They combine
the operator product expansion with the assumption of vacuum condensates, and they
can be used to compute exponentially small corrections to perturbative series in QFT. In the language
of the theory of resurgence, they provide a conjectural method to calculate trans-series in QFT.
If the SVZ approach captures fundamental non-perturbative physics,
it should be able to reproduce trans-series which can be obtained from well-established non-perturbative methods.
In this talk I will provide a general overview of the SVZ approach for the theoretician, and then I will present a precision test
of this approach in the Gross-Neveu model, where exact trans-series can be obtained from large N methods.
I will show that the SVZ method correctly reproduces the first two non-perturbative corrections to the fermion self-energy,
as due to a two-quark and a four-quark condensate, and at all loops.