  Several experiments on tagged molecules or particles in living systems
suggest that they move anomalously slow - their mean squared displacement (MSD)
increase slower than linearly with time. Leading models aimed at understanding
these experiments predict that the MSD grows as a power law with a growth
exponent that is smaller than unity. However, in some experiments the exponent
is so small $(\sim 0.1-0.2)$ that they hint towards other mechanisms at play.
In this paper, we theoretically demonstrate how in-plane collective modes
excited by thermal fluctuations in a two dimensional membrane lead to
logarithmic time dependence for the mean square displacement of a tracer
particle.
