Geometric modular flows in 2d CFT and beyond

TL;DR

This paper investigates geometric modular flows in 2D conformal field theories, showing their conformal equivalence under certain conditions, constructing states from flows, and analyzing energy and entanglement properties, with extensions beyond the Rindler wedge.

Contribution

It provides a method to construct states from geometric modular flows using conformal unitaries and extends the analysis to higher dimensions and beyond the Rindler wedge.

Findings

Generic geometric modular flows in the Rindler wedge are conformally equivalent.

Explicit construction of states from flows using conformal unitaries.

Derived formulas for energy density and entanglement entropy.

Abstract

We study geometric modular flows in two-dimensional conformal field theories. We explore which states exhibit a geometric modular flow with respect to a causally complete subregion and, conversely, how to construct a state from a given geometric modular flow. Given suitable boundary conditions, we find that generic geometric modular flows in the Rindler wedge are conformally equivalent. Based on this insight, we show how conformal unitaries can be used to explicitly construct a state for each flow. We analyze these states, deriving general formulas for the energy density and entanglement entropy. We also consider geometric flows beyond the Rindler wedge setting, and in higher dimensions.