Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories
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Lambert, N., Lipstein, A., Mouland, R., & Richmond, P. (2022). Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories. JHEP, 2022 (2) https://doi.org/10.1007/JHEP02(2022)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 $SU(1,3)\times U(1)$ 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.
Regular Article - Theoretical Physics, Nonperturbative Effects, Conformal Field Theory, M-Theory
External DOI: https://doi.org/10.1007/JHEP02(2022)151
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334202