FOLDS IN 2D STRING THEORIES

We study maps from a 2D world sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space o f folded maps is written down. We show that the latter is not invarian t under area-preserving diffeomorphisms of the target space. The contr ibution to the partition function of maps associated with a given fold configuration is computed. We derive a description of folds in terms of Feynman diagrams. A scheme to sum up the contributions of folds to the partition function in a special case is suggested and is shown to be related to the Baxter-Wu lattice model. An interpretation of folds as trajectories of particles in the adjoint representation of SU(N) ga uge group in the large-N limit which interact in an unusual way with t he gauge fields is discussed.