Abstract
Two-dimensional quantum R2 gravity is studied in the semiclassical way. The thermodynamic properties, such as the equation of state, the temperature and the entropy, are examined. The classical solutions (vacua) of the R2 Liouville equation are obtained by making use of the well-known solution of the ordinary Liouville equation. They are constant curvature solutions. The positive constant curvature solution and the negative one are, after proper infrared regularization, “dual” each other. Each solution has two branches (±). We characterize all phases appearing in all solutions and branches. The topology constraint and the area constraint are properly taken into account. A total derivative term and an infrared regularization play important roles. The topology of a sphere is mainly considered.
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