Abstract
A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ( g 00 = 1, g 01 = g 10 = 0) in the continuum formulation. The constraint T 01 = 0 is solved and used to reduce the problem of field theory to that of quantum mechanics. This reduction can also be proved by using a conformal Ward identity. The amplitude depends on the lengths l 1, l 2 of the boundaries, the proper time T and a non-negative integer m associated with winding modes around the boundaries.
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