Affine Strings

A new model of bosonic strings is considered. An action of the model is the sum of the standard string action and a term describing an interaction of a metric with a linear (affine) connection. The Lagrangian of this interaction is an arbitrary analytic function $f(R)$ of the scalar curvature. This is a classically integrable model. The space of classical solutions of the theory consists from sectors with constant curvature. In each sector the equations of motion reduce to the standard string equations and to an additional constant curvature equation for the linear connection. A bifurcation in the space of all Lagrangians takes place. Quantization of the model is briefly discussed. In a quasiclassical approximation one gets the standard string model with a fluctuating cosmological constant. The Lagrangian $f(R)$, like Morse function, governs transitions between manifolds with different topologies.