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 Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions

“…This resolves a long-standing ambiguity in the role of zero modes in DLCQ theories [14,35]. Moreover, if we identify Fourier modes with instantons in the five-dimensional theory, this implies that only anti-instantons can propagate, which is consistent with the observation that the five-dimensional Lagrangians derived in [7,15] localise onto anti-self-dual field configurations. At three points, dimensional reduction also fixes the functional form of the correlators and implies various sum rules on the Fourier modes which essentially enforce that the sum over Fourier modes can never go positive.…”

“…In this paper we studied scalar correlators of five-dimensional non-Lorentzian theories with a centrally extended SU (1, 3) conformal symmetry. Examples of such theories have recently been constructed in [7,8,15] as Ω-deformed Yang-Mills Lagrangian theories. In particular we solved the Ward identities for general N -point functions.…”

“…Another aim of this paper has been to show how, at least in principle, features of a six-dimensional CFT can be computed from a five-dimensional Lagrangian theory. Indeed the theories obtained in [7,8,15] arose from considering (2, 0) and (1, 0) theories on the conformally compactified spacetime (3.4). In particular we explicitly showed that correlation functions of the the Fourier components of six-dimensional operators, as computed in the six-dimensional theory, solved the five-dimensional Ward identities.…”

“…As described above, our motivation for this paper was a certain class of non-Lorentzian Ω-deformed Yang-Mills gauge theories which admit an SU (1, 3) conformal symmetry and provide the Lagrangians for six-dimensional CFT's conformally compactified along a null direction [7,15]. On the other hand, our results do not rely on this Lagrangian and can potentially apply to any theory with this symmetry.…”

“…At three points, dimensional reduction also fixes the functional form of the correlators and implies various sum rules on the Fourier modes which essentially enforce that the sum over Fourier modes can never go positive. In the case of the gauge theories of [7,15] this implies that instantons cannot be produced. At four points, the functional form in six-dimensions is not fixed and hence for simplicity we consider dimensional reduction of disconnected free correlators and show that the corresponding five-dimensional correlators nontrivially decompose into products of 2-point correlators.…”