I in generalized supergravity

Abstract

Abstract We showed in previous work that for homogeneous Yang–Baxter (YB) deformations of AdS $$_5\times $$ 5 × S $$^5$$ 5 the open string metric and coupling and as a result the closed string density $$e^{-2 \Phi } \sqrt{g}$$ e - 2 Φ g remain undeformed. In this work, in addition to extending these results to the deformation associated with the modified CYBE or $$\eta $$ η -deformation, we identify the Page forms as the open string counterpart for RR fields and demonstrate case by case that the non-zero Page forms remain invariant under YB deformations. We give a physical meaning to the Killing vector I of generalized supergravity and show for all YB deformations: (1) I appears as a current for the center of mass motion on the worldvolume of a D-brane probing the background, (2) I is equal to the divergence of the noncommutativity parameter, (3) I exhibits “holographic” behavior where the radial component of I vanishes at the AdS boundary and (4) in pure spinor formalism I is related to a certain state in the BRST cohomology.