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Dilaton Gravity Coupled to a Nonlinear Sigma Model in $2+ε$ Dimensions

Quantum theory of dilaton gravity coupled to a nonlinear sigma model with a maximally symmetric target space is studied in $2+ε$ dimensions. The ultraviolet stable fixed point for the curvature of the nonlinear sigma model demands a new fixed point theory for the dilaton coupling function. The fixed point of the dilaton coupling is a saddle point similarly to the previous case of the flat target space.