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

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

Abstract

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.

Citation

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. https://doi.org/10.1007/jhep02%282022%29151

• 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
• DOI: https://doi.org/10.1007/jhep02%282022%29151
• Related Public URLs: https://arxiv.org/abs/2109.04829