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

Abstract

We study correlation functions in five-dimensional non-Lorentzian theories with an $SU(1,3)$ conformal symmetry. Examples of such theories have recently been obtained as $\Omega$-deformed Yang-Mills Lagrangians arising from a null reduction of six-dimensional superconformal field theories on a conformally compactified Minkowski space. The correlators exhibit a rich structure with many novel properties compared to conventional correlators in Lorentzian conformal field theories. Moreover, identifying the instanton number with the Fourier mode number of the dimensional reduction offers a hope to formulate six-dimensional conformal field theories in terms of five-dimensional Lagrangian theories. To this end we show that the Fourier decompositions of six-dimensional correlation functions solve the Ward identities of the the $SU(1,3)$ symmetry, although more general solutions are possible. Conversely we illustrate how one can reconstruct six-dimensional correlation functions from those of a five-dimensional theory, and do so explicitly at 2- and 3-points. We also show that, in a suitable decompactification limit $\Omega \to 0$, the correlation functions become those of the DLCQ description.

arXiv comment53 pages, 3 figures

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• Non-Lorentzian Avatars of (1,0) Theories
• Ironing out the crease
• RG Flows and Symmetry Enhancement in Five-Dimensional Lifshitz Gauge Theories
• Instanton Worldlines in Five-Dimensional $\Omega$-Deformed Gauge Theory
• Yangian Symmetry in Five Dimensions
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• From colored gravity to electromagnetism