Speaker
Description
Several one-dimensional models (both relativistic and
non-relativistic) can be solved - at least numerically - by a linear,
thermodynamic Bethe ansatz-like integral equation in specific
settings. Excellent examples are the nonlinear sigma models in an
external field coupled to a conserved charge or the
Lieb-Liniger/Gaudin-Yang models for different couplings. In these
scenarios, it is possible to perturbatively expand the physical
quantities (e.g., the energy density of the particles) in some
specific parameter up to very high orders by using the integral
equation. This expansion is an asymptotic series that contains lots of
hidden analytic information on the exact result. In some cases, this
information is complete, and it is possible to reconstruct the exact
result from the perturbative series only using resummation techniques.
That typically means summing up an infinite number of exponentially
suppressed non-perturbative corrections accessible from the
perturbative data by resurgence theory. In other cases, there is a
mismatch between the exact result and the abovementioned procedure,
which can be explained by a careful analysis of the integral equation
in Fourier space. One can find the missing family of exponential
corrections as well, acquiring a complete understanding of the
analytical structure of the physical quantity in terms of the
expansion variable, at least from the mathematical point of view. The
aim of the talk is a brief summary of this method based on
arXiv:2212.09416.
