Towards Lefschetz Thimbles in Sigma Models, I

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles

Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about nonperturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. Ho...

What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles

This is an introductory level review of recent applications of resurgent trans-series and PicardLefschetz theory to quantum mechanics and quantum field theory. Resurgence connects local perturbative data with global topological structure. In quantum mechanical systems, this program provides a constructive relation between different saddles. For example, in certain cases it has been shown that a...

Graded Poisson - Sigma Models I : Complete Actions and Their Symmetries

The formalism of graded Poisson-Sigma models allows the construction of N = (2, 2) dilaton supergravity in terms of a minimal number of fields. For the gauged chiral U(1) symmetry the full action, involving all fermionic contributions , is derived. The twisted chiral case follows by simple redefinition of fields. The equivalence of our approach to the standard second order one in terms of super...

Pseudoduality in Sigma Models

We revisit classical “on shell” duality, i.e., pseudoduality, in two dimensional conformally invariant classical sigma models and find some new interesting results. We show that any two sigma models that are “on shell” duals have opposite 1-loop renormalization group beta functions because of the integrability conditions for the pseudoduality transformation. A new result states for any two comp...

I-30: Prediction Models in IVF