Non-Lorentzian avatars of (1,0) theories

N Lambert,T Orchard

doi:10.1007/jhep02(2021)205

Abstract

We construct five-dimensional non-Lorentzian Lagrangian gauge field theories with an SU(1, 3) conformal symmetry and 12 (conformal) supersymmetries. Such theories are interesting in their own right but can arise from six-dimensional (1, 0) superconformal field theories on a conformally compactified Minkowski spacetime. In the limit that the conformal compactification is removed the Lagrangians we find give field theory formulations of DLCQ constructions of six-dimensional (1, 0) conformal field theories.

Highlights

Reduction of a six-dimensional Lorentzian field theory can lead to five-dimensional non-Lorentzian field theories, if the compact direction is taken to be null
In section four we present a class of non-Lorentzian gauge theories in 4+1 dimensions with 4(+8)supersymmetries, and an SU(1, 3) conformal symmetry
Our approach is to take the action in [17] where the symmetries are appropriate to six-dimensional (2, 0) supersymmetry and all the fields are in the adjoint representation

Summary

Conformal field theories on Ω-deformed Minkowski space

Some will have explicit x+ dependence and won’t survive a reduction to the zero-Fourier mode sector Such generators will not lead to symmetries of the five-dimensional Lagrangian constructed from the zero-modes, but could still be present in the quantum theory. It was shown in [17] that the reduction to the zeromodes preserves, classically, 3/4 of the supersymmetries and conformal supersymmetries. The Fourier mode number is naturally identified with the instanton number of the five-dimensional gauge theory. It is natural to construct more general (1, 0) supersymmetric conformal field theories, obtained by reduction on Omega-deformed Minkowski space. Compactifying x+ corresponds to the familiar DLCQ matrix model proposals for (1, 0) and (2, 0) theories [20, 21], where the dynamics is described by quantum mechanics on the moduli space of instantons

Six-dimensional conformal multiplets and their reduction

Actions

Supersymmetries

Conformal symmetries

Discussion and conclusion