Geometrical Aspects of Solvable Two Dimensional Models
It was noted that there is a connection between the non-linear two-dimensional (2D) models and the scalar curvature r, i.e. when r = -2 the equations of motion of the Liouville and sine-Gordon models were obtained. Further, solutions of various classical nonlinear 2D models can be obtained from the condition that the appropriate curvature two form Ω = 0, which suggtests that these models are closely related. This relation is explored further in the classical version by obtaining the equations of motion from the evolution equations, the infinite number of conserved quantities, and the common central charge. The Poisson brackets of the solvable 2D models are specified by the Virasoro algebra.
KeywordsCentral Charge Scalar Curvature Poisson Bracket Conformal Field Theory Compact Riemann Surface
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