Conclusion
In Section 4 we saw thatP-lines which are related to Jenkis-Strebel differentials (for example, “harmonic”P-lines) describe a world sheet which has to be created and which has to decay. In Bugajska (1990), 1991) we obtained thatP-line satisfying theP-condition is “associated” to reductions of appropriate holomorphicSL(2, ℂ) bundles (over Riemann surfaces determined by this line) to theSU(2) group. This means (Bugajska, 1990, 1991) that we have to deal withSU(2) bundles over Riemann surfaces equipped with a concrete connectionA. If we interpret this connection as a gauge field of weak interaction (which is responsible for a process of decay), then we see that these completely different approaches yield the same physical situation, namely decay and creation. Moreover, holomorphic quadratic differentials which satisfy theP-condition seem to be just Jenkins-Strebel differentials, or at least most of them (it is still an open question).
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Bugajska, K. Teichmüller spaces of string theory. Int J Theor Phys 32, 1329–1362 (1993). https://doi.org/10.1007/BF00675198
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DOI: https://doi.org/10.1007/BF00675198