A noncommutative sigma-model

Abstract

We begin to study a sigma-model in which both the space-time manifold and the two-dimensional string world-sheet are made noncommutative. The most precise results apply to the case where both the space-time manifold and the two-dimensional string world-sheet are replaced by noncommutative tori. In this situation, we are able to determine when maps between such noncommutative tori exist, to derive the Euler-Lagrange equations, to classify many of the critical points of the Lagrangian, and to study the associated partition function.

27 pages, 1 figure. Minor changes made. Reference to arXiv:0909.4978 added

Cited by in corpus (6)

• The Ricci flow on noncommutative two-tori
• Sigma-model solitons on noncommutative spaces
• Mapping spaces and automorphism groups of toric noncommutative spaces
• Topological and non-topological kink families in non-linear $({\mathbb{S}}^1\times {\mathbb{S}}^1)$-Sigma models
• A noncommutative catenoid
• Functor of Points and Height Functions for Noncommutative Arakelov Geometry