Abstract
We find new homogeneous rr matrices containing supercharges, and use them to find new backgrounds of Yang-Baxter deformed superstrings. We obtain these as limits of unimodular inhomogeneous rr matrices and associated deformations of AdS_2\times2×S^2\times2×T^66 and AdS_5\times5×S^55. Our rr 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.
Highlights
Yang-Baxter sigma models [1, 2] are integrable deformations of sigma models, built on r matrices that solve the classical Yang-Baxter equation
Yang-Baxter deformations broadly come in two types, namely they can be inhomogeneous [5] of homogeneous [6], leading to trigonometric q-deformed [7] or twisted [8] symmetry in the sigma model respectively
4.2.1 Infinite dilation r matrix Starting from the permuted R operator given in equation (4.7) of [12], for the associated r matrix rP we find lim β →∞
Summary
Yang-Baxter sigma models [1, 2] are integrable deformations of sigma models, built on r matrices that solve the classical Yang-Baxter equation. Our results will answer a standing question regarding the existence of unimodular jordanian r matrices for psu(2, 2|4) This question arose out of the study of Weyl invariance of Yang-Baxter sigma models [21]. This is believed to guarantee scale invariance but not Weyl invariance [23,24,25], and it was found that in order for a deformed background to solve the more restrictive standard supergravity equations of motion the r matrix needs to satisfy a unimodularity constraint [21, 25] This led to the question whether it is possible to find unimodular extensions of the well known type of jordanian homogeneous r matrices.
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