Crossing Symmetric Dispersion Relations without Spurious Singularities

Recently, there has been renewed interest in a crossing-symmetric dispersion relation from the 1970s due to its implications for both regular quantum field theory and conformal field theory. However, this dispersion relation introduces nonlocal spurious singularities and requires additional locality constraints for their removal, a process that presents considerable technical challenges. In this Letter, we address this issue by deriving a new crossing-symmetric dispersion relation that is free of spurious singularities, resulting in a compact form of the contact terms in crossing-symmetric blocks. Our results establish a solid foundation for the Polyakov bootstrap in conformal field theories and the crossing-symmetry S-matrix bootstrap in quantum field theories.