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 Ω-deformed Yang-Mills Lagrangians arising from a null reduction of sixdimensional 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 Ω → 0, the correlation functions become those of the DLCQ description.

Observations on BPS observables in 6D

“…One may hope to be able to realise the BPS surface operators within some old and new approaches to the N = (2, 0) theory [103][104][105][106][107][108]. Many of those formulations address the presence of planar surfaces and it would be interesting to look for the richer spectrum of BPS observables found here.…”

Lightlike conformal reduction of 6d (1, 0) theories

“…Inspired by the BLG theory [3,4] and the ABJM theory [5] for M2 branes on R 1,2 with an SO(2, 3) conformal symmetry and an SO (8) and SU(4) R-symmetry respectively, corresponding to isometries of AdS 4 × S 7 and AdS 4 × CP 3 , we may for the M5 brane instead consider theories with symmetries of AdS 7 × S 4 and CP 3 × S 4 respectively. Here CP 3 has SU (1,3) isometry and is a noncompact version of CP 3 .…”

“…The embedding of SU (1,3) in SO (2,6) corresponds to the Hopf fibration of AdS 7 over CP 3 . The dimensionally reduced super Yang-Mills preserves 24 real supercharges and was studied from various viewpoints in [6][7][8] and also generalized to (1,0) superconformal theories in [9].…”