The CHY formulae are a set of remarkable formulae describing the scattering amplitudes of a variety of massless theories, as certain worldsheet integrals, localized on the solutions to certain polynomial equations (scattering equations). These formulae arise from a new class of holomorphic strings called Ambitwistor strings that encode exactly the dynamics of the supergravity (Yang-Mills) modes of string theory. Despite some recent progress by W. Siegel and collaborators, it remains as an open question as to what extent this theory was connected to the full string theory. The most mysterious point being certainly that the localization equations of the ambitwistor string also appear in the zero tension limit of string theory (alpha’ to infinity), which is the opposite limit than the supergravity one (alpha’ to zero). In this talk, I’ll report on some work in progress with E. Casali (Math. Inst. Oxford) and argue that the ambitwistor string is actually a tensionless string. Using some forgotten results on the quantization of these objects, we explain that the quantization of tensionless strings is ambiguous, and can lead either to a higher spin theory, or to the ambitwistor string, hence solving the previously mentioned paradox. In passing, we see that the degenerations of the tensile worldsheet that lead to tensionless strings make connection with Galilean Conformal Algebras and the (3d) BMS algebra.
- Relativity Seminar