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 Ω-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 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 Ω → 0, the correlation functions become those of the DLCQ description.
Highlights
Understanding higher-dimensional conformal field theories (CFT’s) is one of the major challenges of Theoretical Physics
We study correlation functions in five-dimensional non-Lorentzian theories with an SU(1, 3) conformal symmetry
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 SU(1, 3) symmetry, more general solutions are possible
Summary
Understanding higher-dimensional conformal field theories (CFT’s) is one of the major challenges of Theoretical Physics. The resulting five-dimensional theories have a non-Lorentzian Lagrangian description with an SU(1, 3) conformal symmetry, SO(5) R-symmetry, 8 supersymmetries and 16 superconformal symmetries These theories retain a knowledge of the sixth spacetime dimension through a topological U(1) current generated by JI ∼ tr(F ∧ F ). In [16] a large class of five-dimensional Lagrangians with SU(1, 3) conformal symmetry but half as many super and superconformal symmetries were constructed, corresponding to a similar conformally compactified null reduction of (1, 0) CFT’s Of their application to six-dimensional CFT’s, string and M-theory, these Lagrangians form a new class of interacting five-dimensional field theories with novel features which are of interest in their own right. Higher derivative corrections to eleven-dimensional supergravity were studied from various other points of view in [27,28,29]
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