The horocycle regulator: exact cutoff-independence in AdS/CFT

TL;DR

This paper introduces a novel holographic regularization scheme using horocycles in AdS3 that yields finite, cutoff-independent entanglement measures, revealing a non-local dual field theory.

Contribution

It proposes a new horocycle-based regularization method in AdS/CFT that produces exact cutoff-independent entanglement quantities and explores their non-local dual field theories.

Findings

Horocycle regularization yields finite, cutoff-independent entanglement measures.

The dual field theory to this scheme is inherently non-local.

A broad class of such cutoff-independent information measures is described.

Abstract

While the entanglement entropy of a single subregion in quantum field theory is formally infinite and requires regularization, certain combinations of entropies are perfectly finite in the limit that the regulator is removed, the mutual information being a common example. For generic regulator schemes, such as a holographic calculation with a uniform radial cutoff, these quantities show non-trivial dependence on the regulator at finite values of the cutoff. We investigate a holographic regularization scheme defined in three-dimensional anti-de Sitter space constructed from \textit{horocycles}, curves in two-dimensional hyperbolic space perpendicular to all geodesics approaching a single point on the boundary, that leads to finite information measures that are \textit{totally} cutoff-independent, even at finite values of the regulator. We describe a broad class of such information measures, and describe how the field theory dual to the horocycle regulator is inherently non-local.