Killing spinors from classical r-matrices

Abstract

The Yang-Baxter (YB) deformation is a systematic way of performibg integrable deformations of two-dimensional symmetric non-linear sigma models. The deformations can be labeled by classical $r$-matrices satisfying the classical YB equation. This YB deformation is also applicable to type IIB superstring theory defined on ${\mathrm{AdS}}_5\times S^5$. In this case, a simple class of YB deformation is associated with TsT transformations of string backgrounds. The data of this transformation is encoded in an antisymmetric bi-vector $\Theta$ (which is often called $\beta$ field or non-commutativity parameter). In this article, we give a simple recipe for obtaining the explicit expression for the Killing spinors of the TsT transformed background starting from $\Theta$. We moreover discuss the M-theory equivalent of the TsT transformation, allowing us to also give Killing spinors of 11-dimensional backgrounds. We discuss examples of TsT transformed backgrounds starting from flat space, ${\mathrm{AdS}}_5\times S^5$ and ${\mathrm{AdS}}_7\times S^4$. We find that in this way we can relate the $\Omega$-deformation to YB deformations.

arXiv comment50 pages, typos corrected. Version published in J.Phys.A

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Cited by in corpus (6)

• Tri-vector deformations in $d=11$ supergravity
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Non-integrability of the $\Omega$-deformation
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• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations