Wilson lines on noncommutative tori

Abstract

We introduce the notion of a monodromy for gauge fields with vanishing curvature on the noncommutative torus. Similar to the ordinary gauge theory, traces of the monodromies define noncommutative Wilson lines. Our main result is that these Wilson lines are invariant under the Seiberg-Witten map changing the deformation parameter of the noncommutative torus.

4 pages, LaTeX (revtex), it is explained why the costruction of a Wilson line using the path ordered exponent does not apply in the noncommutative case

References in corpus (4)

• String Theory and Noncommutative Geometry
• D-branes and Deformation Quantization
• Comments on Gauge Equivalence in Noncommutative Geometry
• A Path Integral Representation of the Map between Commutative and Noncommutative Gauge Fields

Cited by in corpus (6)

• Quantum Field Theory on Noncommutative Spaces
• BPS equations in N=2, D=5 supergravity with hypermultiplets
• Noncommutative AdS Supergravity in three Dimensions
• Singularities of the Seiberg-Witten map
• Gauge Invariance and Noncommutativity
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory