  We argue that an infinite circumference limit can be obtained in
2-dimensional conformal field theory by adopting $L_0-(L_1+L_{-1})/2$ as a
Hamiltonian instead of $L_0$. The theory obtained has a circumference of
infinite length and hence exhibits a continuous and heavily degenerated
spectrum as well as the continuous Virasoro algebra. The choice of this
Hamiltonian was inspired partly by the so-called sine-square deformation, which
is found in the study of a certain class of quantum statistical systems. The
enigmatic behavior of sine-square deformed systems such as the sharing of their
vacuum states with the closed boundary systems can be understood by the
appearance of an infinite circumference.
