Non-Lorentzian avatars of (1,0) theories

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.

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

“…Indeed a Lagrangian may only manifestly realise some subgroup of the symmetries of the full JHEP02(2022)151 quantum theory, as previously demonstrated by the ABJM theory for M2-branes [13]. In a recent series of papers we have constructed a class of five-dimensional Lagrangians with 12 or 24 superconformal symmetries and a non-Lorentzian SU (1,3) spacetime symmetry [14][15][16], studied their correlators [17] and constructed explicit instanton solutions [18]. In this paper we make a proposal as to how these can be used to provide a path integral construction of correlators of six-dimensional superconformal field theories such as the (2, 0) theory associated to M5-branes.…”

Instanton worldlines in five-dimensional Ω-deformed gauge theory

“…This action is invariant under an SU(1, 3) conformal symmetry [10] and, when fermions are included, 4 supersymmetries and 8 superconformal symmetries. In special cases, corresponding to six-dimensional (2, 0) theory, this is enhanced to 8 supersymmetries and 16 superconformal symmetries [5,6].…”

“…So the first term is convergent if µ A (±∞) = 0. The second term will be convergent if ∂ − Φ → 0 faster than 1/| x| 6 . Lastly we have the contributions from the second term in (6.11):…”

“…These theories are not expected to have a Lagrangian description, at least not in any standard sense. In recent work we have obtained a class of five-dimensional Lagrangian gauge field theories without Lorentz invariance but with up to 3/4 of the maximal supersymmetry [5,6]. They were obtained by considering null reductions of six-dimensional superconformal field theories on an Ω-deformed Minkowski space, which in turn arises as JHEP09(2021)086 a conformal compactification of six-dimensional Minkowski space.…”

“…Note that this is a sufficient but not necessary condition for Φ to be finite away from the worldline, which requires only that µ(τ ) is bounded as τ → ±∞ 6. This can be seen by writingµ = 1 2 (µ(∞) + µ(−∞)) + 1 2 (µ(∞) − µ(−∞)) tanh(τ ) + µ0(τ )where µ0 has a finite integral, performing the integral of the first two terms explicitly, and then using (4.5) for the µ0 contribution.…”