2021/02/15 by Murad Alim, Alim, Murad
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2102.07776
We study difference equations which are obtained from the asymptotic\nexpansion of topological string theory on the deformed and the resolved\nconifold geometries as well as for topological string theory on arbitrary\nfamilies of Calabi-Yau manifolds near generic singularities at finite distance\nin the moduli space. Analytic solutions in the topological string coupling to\nthese equations are found. The solutions are given by known special functions\nand can be used to extract the strong coupling expansion as well as the\nnon-perturbative content. The strong coupling expansions show the\ncharacteristics of D-brane and NS5-brane contributions, this is illustrated for\nthe quintic Calabi-Yau threefold. For the resolved conifold, an expression\ninvolving both the Gopakumar-Vafa resummation as well as the refined\ntopological string in the Nekrasov-Shatashvili limit is obtained and compared\nto expected results in the literature. Furthermore, a precise relation between\nthe non-perturbative partition function of topological strings and the\ngenerating function of non-commutative Donaldson-Thomas invariants is given.\nMoreover, the expansion of the topological string on the resolved conifold near\nits singular small volume locus is studied. Exact expressions for the leading\nsingular term as well as the regular terms in this expansion are provided and\nproved. The constant term of this expansion turns out to be the known\nGromov-Witten constant map contribution.\n