Heriot-Watt Mathematics Report Series
HWM07-6, 30 Jan 2007
Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
M Riccardi and R J Szabo
Abstract
We use twist deformation techniques to analyse the behaviour under
area-preserving diffeomorphisms of quantum averages of Wilson
loops in Yang-Mills theory on the noncommutative
plane. We find that while the classical gauge theory is manifestly
twist covariant, the holonomy operators break the quantum
implementation of the twisted symmetry in the usual formal
definition of the twisted quantum field theory. These results are
deduced by analysing general criteria which guarantee twist invariance
of noncommutative quantum field theories. From this a number of general
results are also obtained, such as the twisted symplectic invariance of
noncommutative scalar quantum field theories with polynomial
interactions and the existence of a large class of holonomy operators
with both twisted gauge covariance and twisted symplectic invariance.
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