Tri-vector deformations on compact isometries

In modern physics, conformal field theories play an important role in describing natural phenomena such as phase transitions. This requires both the search for new conformal field theories and the study of connections between those already known. One of the methods that allows such research, which is the focus of this report, is the method of polyvector Yang-Baxter deformations. With its help, it is possible to find new manifolds of conformal field theories (conformal manifolds). For this, a holographic mapping of a special family of solutions to supergravity equations is used, the image of which will be the conformal manifold, that we want to research. This family is defined by a special deformation of an already existing initial solution of supergravity equations along a polyvector stretched on the tangent space of the initial solution. The polyvector is chosen in such a way that the solution of supergravity deformed along it turns out to be its solution again. It is also important that the properties of the holographic correspondence require only polyvectors stretched on compact isometries of the initial solution for the correct implementation of this method. The most studied example of implementing of this method is using of bivector deformation of ten-dimensional supergravity solutions, which allows us obtaining conformal manifolds after using of holographical mapping on result of bivector deformation. However, despite the simplicity of implementing bivector deformation, its properties prohibit using of non-Abelian compact isometries for constructing of bivector. Nevertheless, it turned out that this problem is not observable for other implementations of polyvector deformations: it was demonstrated that trivector deformations of eleven-dimensional supergravity solutions can be performed along compact isometries. The report will present a more detailed description of the essence of the method of polyvector Yang-Baxter deformations, its bivector implementation, and the problem of compact deformations associated with it. A trivector generalization of this implementation for eleven-dimensional supergravity solutions will be demonstrated, and the absence of the problem of deformations along compact non-Abelian isometries in its case.