Celestial conformal field theory (CCFT) is a conjectured theory living on the celestial sphere of the asymptotic boundary of Minkowski. In analogy to the usual AdS/CFT dictionary, CCFTs would be dual to gravitational theories in the bulk, with bulk scattering amplitudes being dual to correlation functions on the celestial sphere. OPE coefficients are basic building blocks of CFTs which should also have an analogue in CCFTs. It has been shown that CCFT OPEs can be extracted from amplitudes with appropriate wavefunctions for external states, but there's still no direct computation using the CCFT itself since we lack a first principles definition. I will talk about recent work I have done computing these OPEs directly by using twistor strings, circumventing the issue of the target space theory. I will show how the worldsheet CFT of the twistor string gives a realization of the algebra of operators of the CCFT, reproducing the known leading OPE terms, as well as how it can be used to compute further regular terms in the OPE, beyond what is currently known. As a bonus, the worldsheet OPE also organizes the spectrum naturally in terms of the infinite dimensional symmetry algebras of CCFTs. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]

The Cachazo-He-Yuan (CHY) formulas are a remarkable representation of tree-level massless scattering amplitudes. Similarly to the Twistor String formulas, the CHY formula presents amplitudes as an integrals over the moduli space of Riemann surfaces constrained to the solutions of a set of algebraic equations called the scattering equations. But contrary to the Twistor String formulas, they can be written in for any dimension and for a variety of massless theories. Behind the original CHY formula and the scattering equations lies a 2D CFT called the Ambitwistor String, much like the original Twistor String, this is a chiral CFT in which correlators of vertex operators reproduce the CHY formulas and give a geometric interpretation of the scattering equations. The Ambitwistor string possesses a few peculiar characteristics when viewed as a string theory, its low energy efective action is the same as Type II closed strings but the appearance of the scattering equations suggests a high-energy limit has been taken a la Gross and Mende. Besides, its genus one correlation functions are modular invariant but UV divergent since they correspond to 10D SUGRA amplitudes. In this talk I'll talk about a program started with P. Tourkine in which the Ambitwistor String (and other Twistor Strings) are treated as coming from the tensionless limit of classcial string theories. These are know as null strings and have a long history in the literature. I'll review the null string and its supersymmetric extensions and show how the Ambitwistor String can be obtained from a particular gauge fixing of the null string. In doing so, I'll address the issue of possible inequivalent quantizations of the null string and compare it to the case of the usual string and shed a light its relation to the Ambitwistor String.