Difference Equation for Quintic 3-Fold

Abstract

In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type of $q$-difference equations at $Q=0$ and $Q=\infty$. We consider two special cases; the first is the $q$-difference equation of $K$-theoretic $I$-function of the quintic, which is degree 25; we use Adams' method to find the extra 20 solutions at $Q=0$. The second special case is a fuchsian case, which is confluent to the differential equation of the cohomological $I$-function of the quintic. We compute the connection matrix and study the confluence of the $q$-difference structure.

References in corpus (6)

• Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
• Permutation-equivariant quantum K-theory V. Toric $q$-hypergeometric functions
• On Phases of 3d $\mathcal{N}=2$ Chern-Simons-Matter Theories
• On the Quantum K-Theory of the Quintic
• Confluence of quantum $K$-theory to quantum cohomology for projective spaces
• Quantum $K$-theory and $q$-Difference equations

Cited by in corpus (2)

• On the Quantum K-Theory of the Quintic
• Quantum $K$-theory and $q$-Difference equations