Date:
Tue, 21/11/201712:00-13:00
Location:
White Dove Conference Hall at Neve-Shalom
Lecturer: Masazumi Honda,
Affiliation: WIS
Abstract:
Perturbative series in quantum field theory is typically non-convergent.
There is a standard way to resum non-convergent series called Borel resummation.
While perturbative series in typical field theory is expected to be non-Borel summable, it is natural 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 will first discuss that we can show 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 will 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 a half imaginary axis, and the Borel resummations along this direction are the same as exact results. For 3d case, all the singularities in Borel plane can be explained by “complexified SUSY solutions” which formally satisfy SUSY conditions but may not be on original path integral contour. [PRL116,no.21,211601(2016), PRD94, no.2, 025039
(2016) and arXiv:1710.05010]
Additional details of the upcoming Joint
Seminars in Theoretical High Energy Physics
can be found on the following link.
Affiliation: WIS
Abstract:
Perturbative series in quantum field theory is typically non-convergent.
There is a standard way to resum non-convergent series called Borel resummation.
While perturbative series in typical field theory is expected to be non-Borel summable, it is natural 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 will first discuss that we can show 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 will 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 a half imaginary axis, and the Borel resummations along this direction are the same as exact results. For 3d case, all the singularities in Borel plane can be explained by “complexified SUSY solutions” which formally satisfy SUSY conditions but may not be on original path integral contour. [PRL116,no.21,211601(2016), PRD94, no.2, 025039
(2016) and arXiv:1710.05010]
Additional details of the upcoming Joint
Seminars in Theoretical High Energy Physics
can be found on the following link.