# Gradient flows without blow-up for Lefschetz thimbles

## TL;DR

This paper introduces new gradient flows for Lefschetz thimbles that avoid finite-time blow-up, with theoretical analysis and numerical validation demonstrating their effectiveness.

## Contribution

The authors develop and analyze novel gradient flows for Lefschetz thimbles that remain well-defined over time, improving upon existing methods.

## Key findings

- Gradient flows do not blow up in finite time.
- Analytic properties of the new flows are established.
- Numerical tests confirm theoretical predictions.

## Abstract

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. We study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.