Entanglement entropy of SU(3) and SU(2) Yang-Mills theories at finite temperature

We calculate the entanglement entropy using a SU(3) quenched lattice gauge simulation. We find that the entanglement entropy scales as 1/l 2 at small l as in the conformal field theory. Here l is the size of the system, whose degrees of freedom is left after the other part are traced out. The derivative of the entanglement entropy with respect to l hits zero at about l * = 0.6 0.7 fm and vanishes above the length. It may imply that the Yang-Mills theory has the mass gap of the order of 1/l * . Within our statistical errors, no discontinuous change can be seen in the entanglement entropy. We discuss also a subtle point appearing in gauge systems when we divide a system with cuts.