Five-dimensional gauge theories and the local B-model

Abstract

We propose an effective framework for computing the prepotential of the topological B-model on a class of local Calabi--Yau geometries related to the circle compactification of five-dimensional $\mathcal{N}=1$ super Yang--Mills theory with simple gauge group. In the simply-laced case, we construct Picard--Fuchs operators from the Dubrovin connection on the Frobenius manifolds associated to the extended affine Weyl groups of type $\mathrm{ADE}$. In general, we propose a purely algebraic construction of Picard--Fuchs ideals from a canonical subring of the space of regular functions on the ramification locus of the Seiberg--Witten curve, encompassing non-simply-laced cases as well. We offer several precision tests of our proposal. Whenever a candidate spectral curve is known from string theory/brane engineering, we perform non-perturbative comparisons with the gauge theory prepotentials obtained from the K-theoretic blow-up equations, finding perfect agreement. We also employ our formalism to rule out some proposals from the theory of integrable systems of Seiberg--Witten geometries for non-simply laced gauge groups.

42 pages

References in corpus (6)

• The Refined Topological Vertex
• Discrete theta angle from an O5-plane
• Double Bruhat Cells in Kac-Moody Groups and Integrable Systems
• Instantons to the people: the power of one-form symmetries
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Mirror symmetry for extended affine Weyl groups

Cited by in corpus (3)

• Seiberg-Witten curves with O7${}^{\pm }$-planes
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Mirror symmetry for extended affine Weyl groups