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

Published version
Peer-reviewed

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Authors

Lambert, N 
Lipstein, A 
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.

Description

Keywords

Nonperturbative Effects, Conformal Field Theory, M-Theory

Journal Title

JOURNAL OF HIGH ENERGY PHYSICS

Conference Name

Journal ISSN

1029-8479
1029-8479

Volume Title

2022

Publisher

Springer Science and Business Media LLC