2020/06/09 by Li, Zhijin
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2006.05119
A program of wide interest in modern conformal bootstrap studies is to numerically solve general conformal field theories, based on a critical assumption that the dynamics is encoded in the conformal four-point crossing equations and positivity condition. In this letter we propose and verify a novel algebraic property of the crossing equations which provides strong restriction for this program. We show for various types of symmetries \cal G, the crossing equations can be linearly converted into the SO(N) vector crossing equations associated with the SO(N)→ \cal G branching rules and the transformations satisfy positivity condition. The dynamics constrained by the \cal G-symmetric crossing equations combined with positivity condition degenerates to the SO(N) symmetric cases, while the non-SO(N) symmetric theories are not directly solvable without introducing the SO(N) symmetry breaking assumptions on the spectrum.