Thermodynamic Properties, Phases and Classical Vacua of Two Dimensional $R^2$-Gravity

Details Thermodynamic Properties, Phases and Classical Vacua of Two Dimensional $R^2$-Gravity Thermodynamic Properties, Phases and Classical Vacua of Two Dimensional $R^2$-Gravity

1995-08-14

arxiv.org/abs/hep-th/9508060v1

Int.J.Mod.Phys. A11 (1996) 3479-3508

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, Figures are not included

Scientific paper

Two dimensional quantum R$^2$-gravity is formulated in the semiclassical method. The thermodynamic properties,such as the equation of state, the temperature and the entropy, are explained. The topology constraint and the area constraint are properly taken into account. A total derivative term and an infrared regularization play important roles. The classical solutions (vacua) of R$^2$-Liouville equation are obtained by making use of the well-known solution of the ordinary Liouville equation. The positive and negative constant curvature solutions are 'dual' each other. Each solution has two branches($\pm$). We characterize all phases. The topology of a sphere is mainly considered.

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