Resurgence in Supersymmetric Localisable Quantum Field Theories
PDF (Thesis) Accepted Version
1995KbAbstractIn this thesis we consider the application of resurgence and Picard Lefschetz theory to supersymmetric localisable quantum field theories in 2, 3 and 4 dimensions. We consider two problems. First, in the theories we study, observables can be calculated exactly using localization methods, and written hermes kelly wallet replica
in the form of a transseries. However in each non perturbative sector, the associated perturbation series is not asymptotic, seemingly rendering the application of resurgence theory impossible. This problem is solved by deploying a Cheshire Cat analysis; we slightly deform the theory rendering the series asymptotic, perform a resurgence analysis in the deformed theory, and analytically continue the deformation back to 0, returning the non perturbative data in the undeformed theories. This is achieved in N=(2,2) theories in 2 dimensions, and N=2 theories in 3 dimensions. Comments are made about how we might generalize this to 4 dimensional theories. The second problem is the disappearance of the resurgence triangle structure in N = 2 theories on a 3 sphere. This structure is recovered by means of introducing a complex squashing parameter, uncovering a hidden topological angle present in the theory. Finally, in the two above mentioned theories and N = 2 theories in 4 dimensions, a method is given for how to combine a resurgence analysis with additional nonperturbative structures present in these theories to compute non perturbative contributions with different topological charge from the perturbative data.