Entanglement and Renormalization Group Irreversibility of Quantum Field Theory 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.