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Unimodular jordanian deformations of integrable superstrings
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We find new homogeneous r matrices containing supercharges, and use them to find new backgrounds of Yang-Baxter deformed superstrings. We obtain these as limits of unimodular inhomogeneous r matrices and associated deformations of AdS2 x S2 x T6 and AdS5 x S5. Our r matrices are jordanian, but also unimodular, and lead to solutions of the regular supergravity equations of motion. In general our deformations are equivalent to particular non-abelian T duality transformations. Curiously, one of our backgrounds is also equivalent to one produced by TsT transformations and an S duality transformation.
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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.
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