5,867 research outputs found
Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
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.Comment: 23 page
Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
We analyse the symmetries underlying nonassociative deformations of geometry
in non-geometric R-flux compactifications which arise via T-duality from closed
strings with constant geometric fluxes. Starting from the non-abelian Lie
algebra of translations and Bopp shifts in phase space, together with a
suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that
deforms the algebra of functions and the exterior differential calculus in the
phase space description of nonassociative R-space. In this setting
nonassociativity is characterised by the associator 3-cocycle which controls
non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists
to construct maps between the dynamical nonassociative star product and a
family of associative star products parametrized by constant momentum surfaces
in phase space. We define a suitable integration on these nonassociative spaces
and find that the usual cyclicity of associative noncommutative deformations is
replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star
product quantization on phase space together with 3-cyclicity, we formulate a
consistent version of nonassociative quantum mechanics, in which we calculate
the expectation values of area and volume operators, and find coarse-graining
of the string background due to the R-flux.Comment: 38 pages; v2: typos corrected, reference added; v3: typos corrected,
comments about cyclicity added in section 4.2, references updated; Final
version to be published in Journal of Mathematical Physic
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