Abstract:

We consider biscalar conformal fishnet models in arbitrary dimension in the planar limit. On the basis of regularity of correlation functions in these models the graph-building operator is constructed. We find spectrum of scaling dimension at least for some types of Feynman integrals with the help of such an operator. Holographic dual of biscalar fishnet models generalising the Gromov-Sever model (fishchains) at the classical and quantum levels are studied. The spectra of scaling dimensions of these models are obtained, the correspondence between the spectra of fischain and fishnet models on some examples is shown. Planar four-point amplitudes of a six-dimensional non-isotropic fishnet model are studied on the basis of the obtained spectra of scaling dimension. Also we consider dual conformal integrals in six dimensions and study the possibility of constructing a closed iterative expression for the BDS-type amplitudes in six dimensions.

(Based on the materials of the candidate’s dissertation.)