Abstract Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of the conformal invariance. In this article, we discuss the correlation functions of scalar operators in non-relativistic conformal field theories in momentum space. We discuss the solution of conformal Ward identities and express 2,3, and 4-point functions as a function of energy and momentum. We also express the 3- and 4-point functions as the one-loop and three-loop Feynman diagram computations in the momentum space. Lastly, we generalize the discussion to the momentum space correlation functions in the presence of a boundary.
We propose a prescription for describing correlation functions in higher-dimensional defect conformal field theories (DCFTs) by those in ancillary conformal field theories (CFTs) without defects, which is a vast generalization of the image method in two-dimensional boundary CFTs. A correlation function of
n operators inserted away from a defect in a DCFT is represented by a correlation function of
2n operators in the ancillary CFT, each pair of which is placed symmetrically with respect to the defect. We establish the correspondence by matching the constraints on correlation functions imposed by conformal symmetry on both sides. Our method has the potential to shed light on new aspects of DCFTs from the viewpoint of conventional CFTs.
We provide numerical evidence that the low-lying part of the entanglement spectrum of a real-space block (i.e. a single interval) of a one-dimensional quantum many body system at a conformal critical point corresponds to the energy spectrum of a boundary conformal field theory (CFT). This correspondence allows to uncover a subset of the operator content of a conformal field theory by inspection of the entanglement spectrum of a single wave function, thus providing important information on a CFT beyond its central charge. As a practical application we show that for many systems described by a compactified boson CFT, one can infer the compactification radius (governing e.g. the power law decay of correlation functions) of the theory in a simple way based on the entanglement spectrum.