Instantons in ϕ4 theories: transseries, virial theorems, and numerical aspects

We discuss numerical aspects of instantons in two- and three-dimensional 𝜙4 theories with an internal 𝑂⁡(𝑁) symmetry group, the so-called 𝑁-vector model. By combining asymptotic transseries expansions for large arguments with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties is necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in 𝜙4 theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations.