Bosonic symmetries of (2, 0) DLCQ field theories

N Lambert,R Mouland,A Lipstein,P Richmond

doi:10.1007/jhep01(2020)166

N Lambert, R Mouland + Show 2 more

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https://doi.org/10.1007/jhep01(2020)166

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Abstract

We investigate symmetries of the six-dimensional (2, 0) theory reduced along a compact null direction. The action for this theory was deduced by considering M-theory on AdS7× S4 and reducing the AdS7 factor along a time-like Hopf fibration which breaks one quarter of the supersymmetry and reduces the isometry group from SO(6, 2) to SU(3, 1). The boundary theory was previously shown to have 24 supercharges and a Lifshitz scaling symmetry. In this paper, we show that it has four boost-like symmetries and an additional conformal symmetry which furnish a representation of SU(3, 1) when combined with the other bosonic symmetries, providing a nontrivial check of the holographic correspondence.

Highlights

The action for this theory was deduced by considering M-theory on AdS7 × S4 and reducing the AdS7 factor along a time-like Hopf fibration which breaks one quarter of the supersymmetry and reduces the isometry group from SO(6, 2) to SU(3, 1)
The basic idea is to consider M-theory on AdS7 × S4 and write the AdS7 factor as a timelike fibration of a non-compact complex projective space CP3, which breaks one quarter of the supersymmetry and the isometry group from SO(6, 2) to SU(3, 1) [11]
There is a topological charge associated with translations along the null direction, and we show that the Noether charges associated with the new symmetries take a similar form, i.e. they involve integrals over the topological density weighted by functions linear or quadratic in position

Summary

The field theories and background geometry

We can take the special case where Ωij = 0 to obtain These field theories arise, after dimensional reduction along x+, from M5-branes on a spacetime whose metric is [7, 10]1. Since we do not have a lagrangian description for a non-abelian theory of M5-branes in six-dimensions we are forced to consider cases where none of the fields depend the x+ direction. In this case the dynamics is described by five-dimensional super-. In particular taking special cases we have the following types of x+-independent (conformal) Killing vectors: type I (b, 0, 0, 0, 0, 0). One can check that the Killing vectors generated by type I–V close among themselves to form a subalgebra

Minkowski space

Type VI

Type VII

Conclusion

A A six-dimensional origin for the symmetries

V μΨ ΓμΓI