Year: 2020
Type: article
Abstract: According to standard lore, perturbative series of super-renormalizable theories have only instanton singularities. In this paper we show that two-dimensional scalar theories with a spontaneously broken O(N ) symmetry at the classical level, which are super-renormalizable, have an IR renormalon singularity at large N . Since perturbative expansions in these theories are made around the “false vacuum” in which the global symmetry is broken, this singularity can be regarded as a manifestation of the non-perturbative absence of Goldstone bosons. We conjecture that the Borel singularity in the ground state energy of the Lieb-Liniger model is a non-relativistic manifestation of this phenomenon. We also provide en passant a detailed perturbative calculation of the Lieb-Liniger energy up to two-loops, and we check that it agrees with the prediction of the Bethe ansatz.
Source: Journal of High Energy Physics
Authors: Marcos Mariño, Tomás Reis
Institution: University of Geneva
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2995223012