Killing spinors from classical r-matrices

Wednesday, 2 May, 2018

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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 β 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.


Domenico Orlando
Susanne Reffert
Yuta Sekiguchi
Kentaroh Yoshid