$I$ in generalized supergravity

TL;DR

This paper extends the understanding of Yang-Baxter deformations in supergravity, showing invariance of certain forms, interpreting the Killing vector I, and exploring its physical significance in string theory contexts.

Contribution

It generalizes previous results to the $ ext{eta}$-deformation, identifies Page forms as RR field counterparts, and provides a physical interpretation of the Killing vector I in generalized supergravity.

Findings

Open string metric and coupling remain undeformed under YB deformations.

Page forms are invariant under YB deformations and serve as RR field counterparts.

The Killing vector I relates to D-brane motion, noncommutativity divergence, and BRST cohomology.

Abstract

We showed in previous work that for homogeneous Yang-Baxter (YB) deformations of AdS$_5\times$S$^5$, the open string metric and coupling, and as a result the closed string density $e^{-2 \Phi} \sqrt{g}$, remain undeformed. In this work, in addition to extending these results to the deformation associated with the modified CYBE, or $\eta$-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 center of mass motion on the worldvolume of a D-branes 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.