Abstract:
We present a systematic way to consider integrable deformations of the AdS_5 x S^5 superstring. It is based on　classical r-matrices satisfying classical Yang-Baxter equation (CYBE). Then a classical r-matrix corresponds to a gravitational solution that describes a deformed AdS_5 x S^5 geometry. In this talk, we present some examples including the Lunin-Maldacena backgrounds for beta deformations of the N=4 super Yang-Mills theory, the Maldacena-Russo backgrounds for non-commutative gauge theories, and Schroedinger spacetimes dual for non-relativistic conformal field theories. If there is time, we will also discuss Yang-Baxter deformations of AdS_5 x T^{1,1} and 4D Minkowski spacetime.