A noncommutative sigma-model
High Energy Physics - Theory
2011-03-31 v2 Operator Algebras
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.
Cite
@article{arxiv.0903.4241,
title = {A noncommutative sigma-model},
author = {Varghese Mathai and Jonathan Rosenberg},
journal= {arXiv preprint arXiv:0903.4241},
year = {2011}
}
Comments
27 pages, 1 figure. Minor changes made. Reference to arXiv:0909.4978 added