KEK Theory Seminar(Dr. Masazumi Honda)
Perturbative series in quanum field theory is typically divergent.
There is a standard method to resum divergent series called Borel resummation.
While perturbative series in typical field theory is expected to be non-Borel summable,
it is important to ask when perturbative series is Borel summable and if it is non-Borel summable,
what is a correct way to resum the perturbative series.
In my talk I first discuss that we can prove Borel summability of perturbative series
in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians for various observables.
It turns out that exact results in these theories can be obtained by summing over the Borel resummations with every instanton number.
I also discuss perturbative series in general 3d N=2 supersymmetric Chern-Simons matter theory,
which is given by a power series expansion of inverse Chern-Simons levels.
We prove that the perturbative series are always Borel summable along imaginary axis.
It turns out that the Borel resummations along this direction are the same as exact results.
[PRL116,no.21,211601(2016) and arXiv:1604.08653]