๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Simulating non-commutative field theory

โœ Scribed by W. Bietenholz; F. Hofheinz; J. Nishimura

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
510 KB
Volume
119
Category
Article
ISSN
0920-5632

No coin nor oath required. For personal study only.

โœฆ Synopsis

Non-commutative

(NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present numeric results for 2d NC gauge theory of rank 1, which turns out to be renormalizable. The area law for the Wilson loop holds at small area, but at large area we observe a rotating phase, which corresponds t,o an Aharonov-Bohm effect. Next we investigate the NC q54 model in d = 3 and explore its phase diagram.

Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that t,he ordered regime splits into a uniform phase and a phase dominated by stripe patterns.

๐Ÿ“œ SIMILAR VOLUMES

Non-commutative field theories beyond pe
Non-commutative field theories beyond perturbation theory
โœ W. Bietenholz; F. Hofheinz; J. Nishimura ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 472 KB

## Abstract We investigate two models in nonโ€commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we me

Non-topological non-commutativity in str
Non-topological non-commutativity in string theory
โœ S. Guttenberg; M. Herbst; M. Kreuzer; R. Rashkov ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 245 KB

## Abstract Quantization of coordinates leads to the nonโ€commutative product of deformation quantization, but is also at the roots of string theory, for which spaceโ€time coordinates become the dynamical fields of a twoโ€dimensional conformal quantum field theory. Appositely, open string diagrams pro