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In this paper we calculate the entanglement entropy of two coupled gaplesssystems in general spatial dimension d. The gapless systems can be eitherconformal field theories (CFT), or Fermi liquids. We assume the two systems arecoupled uniformly in a h-dimensional submanifold of the space, with 0 <= h <=d. We will focus on the scaling of the entanglement entropy with the size ofthe system, and its scaling with the inter-system coupling constant g. Threeapproaches will be used for our calculation: (1) exact calculation with groundstate wave-functional, (2) perturbative calculation with functional pathintegral, (3) scaling argument.

Entanglement Entropy of Coupled Conformal Field Theories and Fermi Liquids