Universality of the topological string at large radius and NS-brane resurgence. (English) Zbl 1364.81203
Summary: We show that there is a natural universal limit of the topological string free energies at the large radius point. The new free energies keep a nonholomorphic dependence on the complex structure moduli space and their functional form is the same for all Calabi-Yau geometries, compact and noncompact alike. The asymptotic nature of the free energy expansion changes in this limit due to a milder factorial growth of its coefficients, and this implies a transseries extension with instanton effects in \(\exp (- 1/g_s^2)\), of NS-brane type, rather than \(\exp (-1/g_s)\), of D-brane type. We show a relation between the instanton action of NS-brane type and the volume of the Calabi-Yau manifold which points to a possible interpretation in terms of NS5-branes. A similar rescaling limit has been considered recently leading to an Airy equation for the partition function which is here used to explain the resurgent properties of the rescaled transseries.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T45 | Topological field theories in quantum mechanics |
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
| 34E10 | Perturbations, asymptotics of solutions to ordinary differential equations |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
Keywords:
topological string theory; mirror symmetry; asymptotics; resurgence; universality; NS-braneReferences:
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