Probing the Moduli Dependence of Refined Topological Amplitudes

Abstract

With the aim of providing a worldsheet description of the refined topological string, we continue the study of a particular class of higher derivative couplings $F_{g,n}$ in the type II string effective action compactified on a Calabi-Yau threefold. We analyse first order differential equations in the anti-holomorphic moduli of the theory, which relate the $F_{g,n}$ to other component couplings. From the point of view of the topological theory, these equations describe the contribution of non-physical states to twisted correlation functions and encode an obstruction for interpreting the $F_{g,n}$ as the free energy of the refined topological string theory. We investigate possibilities of lifting this obstruction by formulating conditions on the moduli dependence under which the differential equations simplify and take the form of generalised holomorphic anomaly equations. We further test this approach against explicit calculations in the dual heterotic theory.

30 pages

References in corpus (7)

• The Refined Topological Vertex
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Instanton calculus in R-R background and the topological string
• M String, Monopole String and Modular Forms
• Threshold corrections, generalised prepotentials and Eichler integrals
• N=4 Topological Amplitudes and String Effective Action
• Harmonicity in N=4 supersymmetry and its quantum anomaly

Cited by in corpus (9)

• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• Self-Duality and Self-Similarity of Little String Orbifolds
• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• Instanton Corrections for m and Omega
• $\Omega$ versus Graviphoton
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras