Abstract
We consider the situation when a globally defined four-dimensional field
system is separated on two entangled sub-systems by a dynamical (random)
two-dimensional surface. The reduced density matrix averaged over ensemble of
random surfaces of fixed area and the corresponding average entropy are
introduced. The average entanglement entropy is analyzed for a generic
conformal field theory in four dimensions. Two important particular cases are
considered. In the first, both the intrinsic metric on the entangling surface
and the spacetime metric are fluctuating. An important example of this type is
when the entangling surface is a black hole horizon, the fluctuations of which
cause necessarily the fluctuations in the spacetime geometry. In the second
case, the spacetime is considered to be fixed. The detail analysis is carried
out for the random entangling surfaces embedded in flat Minkowski spacetime. In
all cases the problem reduces to an effectively two-dimensional problem of
random surfaces which can be treated by means of the well-known conformal
methods. Focusing on the logarithmic terms in the entropy we predict the
appearance of a new \$łnłn(A)\$ term.
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