On Galilean conformal bootstrap

In this work, we develop conformal bootstrap for Galilean field theory (GCFT). a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from usual theory, quasi-primary in GCFT constitute multiplets, which are block-diagonized under boost operator. More importantly multiplets include of negative norms, indicating is not unitary. We compute blocks discuss expansion four-point functions terms multiplets. Furthermore do harmonic analysis symmetry obtain an inversion formula. As first step to apply bootstrap, construct generalized free (GGFT) explicitly. read data GGFT by using Taylor series function formula independently, find exact agreement. some novel features due non-semisimpleness algebra non-unitarity GCFTs.