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# (08.11.) Killing spinors from classical r-matrices

### Yuta Sekiguchi (Bern)

#### 08.11.2018 at 16:15

The Yang-Baxter (YB) deformation is a systematic way of providing integrable deformations of two-dimensional symmetric non-linear sigma models. Such deformations can be labeled by classical r-matrices satisfying the classical YB equation. This YB deformation can also be applied to type IIB superstrings on AdS5xS5, where a simple class of YB deformation is associated with the TsT transformation of string backgrounds. The data of this transformation is encoded in an antisymmetric bi-vector \Theta, called non-commutativity parameter. In this talk, after some brief review of YB deformations, I will present a simple recipe for explicitly obtaining the Killing spinors in the TsT deformed backgrounds starting from \Theta by giving various examples. Consequently, the Killing spinors are expressed only by \Theta and constant with respect to the Kosmann Lie derivative. Then I will comment on the recent developments focusing on the non-abelian classical r-matrices. This talk is mainly based on 1805.00948 and work in progress.

Arnold Sommerfeld Center

Theresienstrasse 37

Room 348