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

DOI10.1007/JHEP03(2021)053zbMATH Open1461.81110arXiv2012.00626OpenAlexW3108391333MaRDI QIDQ2028255

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Publication date: 31 May 2021

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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 $Omegao0$, the correlation functions become those of the DLCQ description.

Full work available at URL: https://arxiv.org/abs/2012.00626

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