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.
Highlights
Quantum theory, as previously demonstrated by the ABJM theory for M2-branes [13]
We have seen that the five-dimensional path integral based on the Lagrangian (2.1) leads to a theory with an SU(1, 3) × U(1) symmetry that acts non-trivially on a Kaluza-Klein-like tower of operators obtained by inserting instantons
In this paper we have explored how the path integral based on five-dimensional Lagrangians with an SU(1, 3) spacetime symmetry can be used to reconstruct correlation functions of a six-dimensional conformal field theory
Summary
We review the five-dimensional Ω-deformed gauge theory first introduced in [14] by a reduction of the (2, 0) theory, and recast its known spacetime symmetries [15] in a language more useful for this paper. There are (1, 0) versions of these actions where the fields further decompose into tensor and hyper multiplets and the supersymmetries are reduced by a half [16]. The form of the action and symmetries is similar but the hyper multiplet fields are allowed to take values in any representation of the gauge group. In the interests of not introducing additional notation we will not discuss them here since all the results in this paper extend directly to these theories too as the main tool we exploit is the SU(1, 3) symmetry of the action
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
