Abstract
In recent years, great progress has been made on a systematic method to perform an integrable deformation of a two-dimensional relativistic non-linear sigma model. The deformations are labeled by classical r-matrices satisfying the classical Yang-Baxter equation, and this method is called the Yang-Baxter deformation. It was generalized to type IIB superstring theory defined on the AdS\(_5\,\times \,\)S\(^5\) background and gave rise to a lot of integrable backgrounds including well-known backgrounds such as the Lunin-Maldacena background, a gravity dual for a non-commutative gauge theory, and a Schr\(\ddot{\mathrm{o}}\)dinger spacetime. In addition, the study of Yang-Baxter deformation led to the discovery of a generalized type IIB supergravity. In this proceeding, I will give a short summary of the recent progress on the Yang-Baxter deformation and the generalized supergravity.
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