Immersions and folds in string theories of gauge fields

A two-dimensional string model with dynamical cancellation of folds is considered. The action of the model contains the self-intersection number which is defined for surfaces immersed into 4D targets. The two additional variables are not dynamical and live on a compact manifold. In this sense the model is a compactification of a 4D theory. The cancellation forces the string $þ$ angle to be equal $π$. Candidates for string states are constructed. Some mathematical background is given.

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