2D Quantum Gravity in the Proper-Time Gauge

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.

12 pages, latex

References in corpus (2)

• Transfer Matrix Formalism for Two-Dimensional Quantum Gravity and Fractal Structures of Space-time
• String Field Theory of Noncritical Strings

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