Towards Lefschetz thimbles in Sigma models, I

Abstract

We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the $O(N)$ and ${\mathbf{CP}}^{N-1}$ models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite temperature, with various chemical potentials corresponding to the symmetries of the models. In this paper we discuss the case of the $O(2m)$ and the ${\mathbf{CP}}^{N-1}$ models in the sector of zero instanton charge, as well as some solutions of the $O(2m+1)$ model. The ${\mathbf{CP}}^{N-1}$-model for all instanton charges and a more general class of solutions of the $O(N)$-model with odd $N$ will be discussed in the forthcoming paper.

arXiv comment38 pages

References in corpus (7)

• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Branes and N=2 Theories in Two Dimensions
• Holomorphic Bundles and Many-Body Systems
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• CP(N) sigma model on a finite interval revisited
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• A Journey Between Two Curves

Cited by in corpus (4)

• Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model
• Novikov-Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model
• Novel aspects of integrability for NLSMs in symmetric spaces
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory