Resurgence for general (possibly infinite-dimensional) thimble integrals

Establish that for thimble integrals I_a = ∫_{𝒞_a^θ} e^{-z f} ν, associated to holomorphic maps f from complex manifolds X to translation surfaces B, without assuming that f is a holomorphic Morse function and allowing possibly infinite-dimensional analogues, the position-domain function ι_a obtained by the thimble projection formula is resurgent; equivalently, show that the Borel transform of the asymptotic expansion of I_a is endlessly analytically continuable. This would extend the known Morse-case result asserting resurgence of ι_a.

Background

The paper explains that for one-dimensional thimble integrals with a holomorphic Morse function in the exponent, geometric arguments imply that the corresponding position-domain function (the Borel transform obtained via the thimble projection formula) is resurgent. This provides a rigorous link between thimble integrals and the analytic structure captured by resurgence theory.

It is conjectured that this resurgence property persists beyond the Morse setting to more general thimble integrals, and possibly even to infinite-dimensional settings relevant to quantum field theory. Formalizing and proving this extension would generalize current results and clarify the scope of resurgence phenomena in geometric and physical applications.