Five-dimensional non-Lorentzian conformal field theories and their relation to six-dimensions


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.

Journal of High Energy Physics 03 (2021) 053
Rishi Mouland
Rishi Mouland
Research Associate in High Energy Theoretical Physics

My research interests include string theory, M-theory and conformal field theory