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

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


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.

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Publisher 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.
Date accepted:02 February 2022
Date deposited:23 February 2022
Date of first online publication:17 February 2022
Date first made open access:23 February 2022

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