Five-dimensional path integrals for six-dimensional conformal field theories

N. Lambert, A. Lipstein*, R. Mouland, P. Richmond

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
18 Downloads (Pure)


In this paper we derive Ward-Takahashi identities from the path integral of supersymmetric five-dimensional field theories with an SU(1, 3) spacetime symmetry in the presence of instantons. We explicitly show how SU(1, 3) is enhanced to SU(1, 3) × U(1) where the additional U(1) acts non-perturbatively. Solutions to such Ward-Takahashi identities were previously obtained from correlators of six-dimensional Lorentzian conformal field theories but where the instanton number was replaced by the momentum along a null direction. Here we study the reverse procedure whereby we construct correlation functions out of towers of five-dimensional operators which satisfy the Ward-Takahashi identities of a six-dimensional conformal field theory. This paves the way to computing observables in six dimensions using five-dimensional path integral techniques. We also argue that, once the instanton sector is included into the path integral, the coupling of the five-dimensional Lagrangian must be quantised, leaving no free continuous parameters.

Original languageEnglish
Article number151
JournalJournal of High Energy Physics
Issue number2
Publication statusPublished - 17 Feb 2022


  • Conformal Field Theory
  • M-Theory
  • Nonperturbative Effects


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