Holography for chiral scale-invariant models

TL;DR

This work develops a holographic framework for chiral, scale-invariant models with dynamical exponent $z$, showing that deforming a CFT by a constant null vector source for a vector operator of dimension $(d+z-1)$ yields AdS plane-wave geometries and an exactly marginal deformation under the anisotropic symmetry. The authors construct and analyze the bulk massive-vector models, derive holographic renormalization rules in $d=2$, and determine the linearized spectra around the chiral background, identifying non-dynamical 'T' modes and propagating 'X' modes whose correlators encode the boundary stress tensor and deforming-vector data. They provide explicit results for two-point functions, Ward identities, and the structure of counterterms, including how the UV behavior changes for $z>1$ and the special cases $z=2$ (Schrödinger) and $z=0$ (Lifshitz upon null DLCQ). The analysis also includes black-hole solutions asymptotic to the chiral background, reinforcing the finite-temperature interpretation and highlighting the role of the deforming operator across the phase structure. Overall, the paper maps the holographic dictionary for these anisotropic theories and illuminates how exactly marginal deformations shape correlators and renormalization, with implications for non-relativistic holography and potential string-theoretic embeddings.

Abstract

Deformation of any d-dimensional conformal field theory by a constant null source for a vector operator of dimension (d + z -1) is exactly marginal with respect to anisotropic scale invariance, of dynamical exponent z. The holographic duals to such deformations are AdS plane waves, with z=2 being the Schrodinger geometry. In this paper we explore holography for such chiral scale-invariant models. The special case of z=0 can be realized with gravity coupled to a scalar, and is of particular interest since it is related to a Lifshitz theory with dynamical exponent two upon dimensional reduction. We show however that the corresponding reduction of the dual field theory is along a null circle, and thus the Lifshitz theory arises upon discrete light cone quantization of an anisotropic scale invariant field theory.