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

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

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N. Lambert

R. Mouland

P. Richmond


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.


Lambert, N., Lipstein, A., Mouland, R., & Richmond, P. (2022). Five-dimensional path integrals for six-dimensional conformal field theories. Journal of High Energy Physics, 2022(2), Article 151.

Journal Article Type Article
Acceptance Date Feb 2, 2022
Online Publication Date Feb 17, 2022
Publication Date 2022-02
Deposit Date Feb 22, 2022
Publicly Available Date Feb 23, 2022
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2022
Issue 2
Article Number 151
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Copyright Statement
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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