Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories
| Autor: | Lambert, Neil, Lipstein, Arthur, Mouland, Rishi, Richmond, Paul |
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| Rok vydání: | 2021 |
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| Zdroj: | JHEP 02 (2022) 151 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP02(2022)151 |
| Popis: | 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. Comment: 40 pages. Technical details added in Section 3, and notation adjusted. Matches JHEP published version |
| Databáze: | arXiv |
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