Trans-series from condensates in the non-linear sigma model

Abstract

In this work we provide a massless perturbative framework for the two dimensional non-linear sigma model (NLSM), that allows the computation of the perturbative series attached to the operator condensates in the operator product expansion (OPE). It is based on a limit of the quartic linear sigma model (LSM) and is manifestly $O(N)$ symmetric. We show, at next-to-leading order in the $1/N$ expansion, how this framework reproduces the perturbative contribution to the two-point function, as well as its first exponentially small correction due to the condensate of the Lagrangian operator, in full agreement with the exact non-perturbative large $N$ solution. We also show that, in the full LSM, the physics at the natural UV cutoff indeed decouples from the NLSM in the IR, in the weak-coupling limit. In particular, we show that the perturbative framework for the LSM at the cutoff scale is connected to the one in the NLSM. The structure of power divergences in the LSM regularization also reveals that the first renormalon on the positive Borel axis of the NLSM perturbative self-energy is an UV renormalon, which cancels against the ambiguity in the condensate.

40 pages, 8 figures; v2: reorganized sections for improved clarity of exposition. Minor corrections and clarifications added. Results unchanged

References in corpus (25)

• Renormalons
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• Compelling evidence of renormalons in QCD from high order perturbative expansions
• $\lambda {\varphi }^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO
• Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory
• The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $\sigma$-Model
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• New renormalons from analytic trans-series
• Testing the Bethe ansatz with large N renormalons
• A new renormalon in two dimensions
• Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling
• Instantons, renormalons and the theta angle in integrable sigma models
• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
• Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$
• Operator Product Expansion on the Lattice: a Numerical Test in the Two-Dimensional Non-Linear Sigma-Model
• Structure functions of the 2d O(n) non-linear sigma models
• Renormalons: technical introduction
• Non-Perturbative Renormalization in Lattice Field Theory
• Trans-series from condensates
• On the Structure of Trans-Series in Quantum Field Theory
• Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model
• Anatomy of the simplest renormalon
• Wiener-Hopf solution of the free energy TBA problem and instanton sectors in the O(3) sigma model
• From Operator Product Expansion to Anomalous Dimensions