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.
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Tanizaki, Y., Nishimura, H., & Verbaarschot, J. J. M. (2017). Gradient flows without blow-up for Lefschetz thimbles. Journal of High Energy Physics, 2017(10). https://doi.org/10.1007/JHEP10(2017)100