LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Towards Lefschetz Thimbles in Sigma Models, I

Photo by googledeepmind from unsplash

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 $$\mathbb{C}{{\mathbb{P}}^{{N - 1}}}$$ models,… Click to show full abstract

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 $$\mathbb{C}{{\mathbb{P}}^{{N - 1}}}$$ 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 (2 m ) and the $$\mathbb{C}{{\mathbb{P}}^{{N - 1}}}$$ models in the sector of zero instanton charge, as well as some solutions of the O (2 m + 1) model. The $$\mathbb{C}{{\mathbb{P}}^{{N - 1}}}$$ -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.

Keywords: towards lefschetz; sigma models; lefschetz thimbles; thimbles sigma; mathbb mathbb

Journal Title: Journal of Experimental and Theoretical Physics
Year Published: 2020

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.