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Space-time CFTs from the Riemann sphere

  • Tim Adamo
  • Ricardo Monteiro
  • Miguel F. Paulos
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Conformal Field Models in String Theory Conformal Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Tim Adamo
    • 1
  • Ricardo Monteiro
    • 2
    • 3
  • Miguel F. Paulos
    • 3
  1. 1.Theoretical Physics GroupBlackett Laboratory, Imperial College LondonLondonUnited Kingdom
  2. 2.Centre for Research in String TheoryQueen Mary University of LondonLondonUnited Kingdom
  3. 3.Theoretical Physics DepartmentCERNGeneva 23Switzerland

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