Abstract
We review some perturbative and nonperturbative aspects of topological string theory on the Calabi–Yau manifolds X p =O(−p)⊕ O(p−2)→ℙ1. These are exactly solvable models of topological string theory which exhibit a nontrivial yet simple phase structure, and have a phase transition in the universality class of pure two-dimensional gravity. They don’t have conventional mirror description, but a mirror B model can be formulated in terms of recursion relations on a spectral curve typical of matrix model theory. This makes it possible to calculate nonperturbative, spacetime instanton effects in a reliable way, and in particular to characterize the large order behavior of string perturbation theory.
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Mariño, M. (2009). Topological Strings on Local Curves. In: Sidoravičius, V. (eds) New Trends in Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2810-5_31
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DOI: https://doi.org/10.1007/978-90-481-2810-5_31
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