Star products built from active symmetry transformations give gauge-invariant non-commutative theories under a weakened unimodularity condition, with a planar equivalence theorem keeping internal Feynman structure undeformed.
On Yang-Baxter models, twist operators, and boundary conditions
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We discuss homogeneous Yang-Baxter deformations of integrable sigma models in terms of twist operators. We show that the twist operators behave as the classical analogue of a Drinfeld twist, for all abelian and almost abelian deformations. We also use twist operators to rederive the well-known interpretation of TsT transformations -- equivalent to abelian deformations -- in terms of twisted boundary conditions. We discuss complications in extending this boundary condition picture to non-abelian deformations.
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A new perspective on non-commutative deformations of field and gauge theories
Star products built from active symmetry transformations give gauge-invariant non-commutative theories under a weakened unimodularity condition, with a planar equivalence theorem keeping internal Feynman structure undeformed.