TY - JOUR
T1 - Entanglement entropy in all dimensions
AU - Braunstein, Samuel Leon
AU - Das, Saurya
AU - Shankaranarayanan, S
PY - 2013/7/22
Y1 - 2013/7/22
N2 - It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the Rényi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic degrees of freedom inside and outside hypersurfaces. For the first time, we show that the entanglement entropy in higher dimensions is proportional to the higher dimensional area. We also show that the Rényi entropy diverges at specific values of the Rényi parameter q in each dimension, but this divergence can be tamed by introducing a mass to the quantum field.
AB - It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the Rényi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic degrees of freedom inside and outside hypersurfaces. For the first time, we show that the entanglement entropy in higher dimensions is proportional to the higher dimensional area. We also show that the Rényi entropy diverges at specific values of the Rényi parameter q in each dimension, but this divergence can be tamed by introducing a mass to the quantum field.
U2 - 10.1007/JHEP07(2013)130
DO - 10.1007/JHEP07(2013)130
M3 - Article
SN - 1029-8479
VL - 130
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 07
M1 - 130
ER -