Space-time CFTs from the Riemann sphere

Abstract

We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer dimensions. These theories have a SL(2) algebra of local bosonic constraints which can be supplemented by additional fermionic constraints depending on the matter content of the theory. By computing the BRST charge associated with gauge fixing these constraints, we find anomalies which vanish for specific target space dimensions. These critical dimensions coincide precisely with those for which (biadjoint) cubic scalar theory, gauge theory and gravity are classically conformally invariant. Furthermore, the BRST cohomology of each theory contains vertex operators for the full conformal multiplets of single field insertions in each of these space-time CFTs. We give a prescription for the computation of three-point functions, and compare our formalism with the scattering equations approach to on-shell amplitudes.

34 pages, no figures. v2: typos corrected and some comments added; v3: published version

References in corpus (12)

• Writing CFT correlation functions as AdS scattering amplitudes
• Ambitwistor strings in 4-dimensions
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• A Worldsheet Theory for Supergravity
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Connected formulas for amplitudes in standard model
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• A note on connected formula for form factors
• The connected prescription for form factors in twistor space
• On Form Factors and Correlation Functions in Twistor Space
• Composite operators and form factors in N=4 SYM
• Correlation functions of the chiral stress-tensor multiplet in N=4 SYM

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• Ambitwistor Strings in Six and Five Dimensions
• Massless spinning particle and null-string on $Ad{S}_d$: projective-space approach
• Ambitwistor strings and amplitudes in curved backgrounds