Nonperturbative phenomena in field theory and gravity, and use of Borel summation to capture nonperturbative information

Abstract

This thesis addresses non-perturbative phenomena and techniques to analyze nonperturbative problems. First, we discuss the simplest non-perturbative example in quantum gravity: blackholes, and how they non-perturbatively emit Hawking Radiation. This is directly linked to the blackhole information paradox. We then discuss non-perturbative phenomena in quantum eld theory. In particular, we discuss instantons in Yang-Mills and large-N sigma models. We discuss Borel summation as a technique to capture non-perturbative terms in a perturbative expansion. We apply Borel summation to the simple Painleve-I system and solve it numerically.