Entanglement and Renormalization Group Irreversibility of Quantum Field Theory in AdS

TL;DR

This paper investigates the irreversibility of renormalization group flows in quantum field theories within anti de Sitter spacetime using quantum information methods, establishing new inequalities and analyzing specific models.

Contribution

It derives an entropic inequality for QFTs in AdS, proving RG irreversibility in multiple dimensions and developing lattice methods for entanglement calculations.

Findings

Proves RG irreversibility in 2, 3, and 4 dimensions.

Derives an entropic second-order differential inequality.

Provides analytic and numerical results for free fermions in AdS.

Abstract

We study nonperturbative aspects of quantum field theory (QFT) in rigid anti de Sitter (AdS) spacetime using quantum information theoretic methods. While irreversibility of renormalization group (RG) flows is well established in flat space, it is not obvious whether it persists in AdS, where negative curvature and an asymptotic timelike boundary significantly modify infrared dynamics. Using strong subadditivity and AdS invariance, we derive an entropic second-order differential inequality for the difference between the vacuum entanglement entropy of a QFT and that of its ultraviolet fixed point, evaluated for spherical bulk regions. This inequality allows us to define RG charges that measure the relevant number of degrees of freedom, and we prove the irreversibility of the RG in $2,\,3,$ and $4$ spacetime dimensions. We further analyze free scalar and fermion theories in AdS, developing lattice formulations adapted to the geometry and computing entanglement entropies and RG charges. In AdS$_2$, we obtain analytic results for a massive Dirac fermion and compare them with numerical lattice calculations. These examples illustrate the general irreversibility theorem and clarify the distinction between conformal and massive theories in AdS.