an:06428074
Zbl 1316.81075
Alim, Murad; Scheidegger, Emanuel
Topological strings on elliptic fibrations
EN
Commun. Number Theory Phys. 8, No. 4, 729-800 (2014).
00343042
2014
j
81T30 14D06 14J33 14J32
topological string theory; elliptically fibered Calabi-Yau manifolds; mirror symmetry; modular forms
Authors' summary: We study topological string theory on elliptically fibered Calabi-Yau manifolds using mirror symmetry. We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the special geometry of the deformation spaces. The polynomials are fixed by the holomorphic anomaly equations supplemented by the expected behavior at special loci in moduli space. We further expand the amplitudes in the base moduli of the elliptic fibration and find that the fiber moduli dependence is captured by a finer polynomial structure in terms of the modular forms of the modular group of the elliptic curve. We further find a recursive equation which captures this finer structure and which can be related to the anomaly equations for correlation functions.
Jochen Zahn (Leipzig)