Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories
Publication Date
2022-02Journal Title
JHEP
ISSN
1126-6708
Publisher
Springer Science and Business Media LLC
Volume
2022
Issue
2
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
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
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 $SU(1,3)\times U(1)$ 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.
Keywords
Regular Article - Theoretical Physics, Nonperturbative Effects, Conformal Field Theory, M-Theory
Identifiers
jhep02(2022)151, 17836
External DOI: https://doi.org/10.1007/JHEP02(2022)151
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334202
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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