On Galilean conformal bootstrap. Part II. ξ = 0 sector
Bin Chen (Center for High Energy Physics, Peking University, No.5 Yiheyuan Rd, Beijing, 100871, P.R. China, Collaborative Innovation Center of Quantum Matter, No.5 Yiheyuan Rd, Beijing, 100871, P.R. China, School of Physics, Peking University, No.5 Yiheyuan Rd, Beijing, 100871, P.R. China); Peng-xiang Hao (Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, P.R. China); Reiko Liu (School of Physics, Peking University, No.5 Yiheyuan Rd, Beijing, 100871, P.R. China); Zhe-fei Yu (Center for High Energy Physics, Peking University, No.5 Yiheyuan Rd, Beijing, 100871, P.R. China)
In this work, we continue our work on two dimensional Galilean conformal field theory (GCFT2). Our previous work (2011.11092) focused on the ξ ≠ 0 sector, here we investigate the more subtle ξ = 0 sector to complete the discussion. The case ξ = 0 is degenerate since there emerge interesting null states in a general ξ = 0 boost multiplet. We specify these null states and work out the resulting selection rules. Then, we compute the ξ = 0 global GCA blocks and find that they can be written as a linear combination of several building blocks, each of which can be obtained from a sl(2, ℝ) Casimir equation. These building blocks allow us to give an Euclidean inversion formula as well. As a consistency check, we study 4-point functions of certain vertex operators in the BMS free scalar theory. In this case, the ξ = 0 sector is the only allowable sector in the propagating channel. We find that the direct expansion of the 4-point function reproduces the global GCA block and is consistent with the inversion formula.
