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

We discuss numerical aspects of instantons in two- and three-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>ϕ</a:mi><a:mn>4</a:mn></a:msup></a:math> theories with an internal <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>O</c:mi><c:mo stretchy="false">(</c:mo><c:mi>N</c:mi><c:mo stretchy="false">)</c:mo></c:math> symmetry group, the so-called <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>N</g:mi></g:math>-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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>ϕ</i:mi><i:mn>4</i:mn></i:msup></i:math> theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. Published by the American Physical Society 2024