Anisotropic conformal Carroll field theories and their gravity duals

TL;DR

This paper explores anisotropic conformal Carroll field theories with zero dynamical exponent and their gravity duals, revealing infinite-dimensional symmetries and proposing a holographic correspondence via plane wave geometries.

Contribution

It constructs the Carrollian stress tensor, analyzes correlation functions, and identifies gravity duals with isometry algebras matching the Carroll symmetries, establishing a new holographic framework.

Findings

Carrollian stress tensor with specific transformation properties

Correlation functions depend on vacuum choices

Gravity duals are plane wave geometries with matching symmetries

Abstract

We investigate anisotropic conformal Carroll field theories and their holographic duals. On the field theory side, we focus on the case with scaling exponent $z=0$ in two and three spacetime dimensions. These theories exhibit infinite-dimensional symmetry algebras, including supertranslations and superrotations, and are closely related to, but distinct from, Warped Conformal Field Theories. We construct the associated Carrollian stress tensor, derive its transformation properties, and analyse the structure of correlation functions under different choices of vacua. On the gravity side, we identify three and four-dimensional plane wave geometries whose isometry algebras realise the two- and three-dimensional Carroll algebra and anisotropic scale transformations. We propose, for each scaling exponent, a phase space of asymptotically-plane wave spacetimes and show that the residual diffeomorphisms reproduce the expected conformal Carroll field theory algebra, establishing a framework for anisotropic Carrollian holography.