Fivedimensional gauge theories and the local Bmodel
Abstract
We propose an effective framework for computing the prepotential of the topological Bmodel on a class of local CalabiYau geometries related to the circle compactification of fivedimensional $\mathcal{N}=1$ super YangMills theory with simple gauge group. In the simplylaced case, we construct PicardFuchs 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 PicardFuchs ideals from a canonical subring of the space of regular functions on the ramification locus of the SeibergWitten curve, encompassing nonsimplylaced 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 nonperturbative comparisons with the gauge theory prepotentials obtained from the Ktheoretic blowup equations, finding perfect agreement. We also employ our formalism to rule out some proposals from the theory of integrable systems of SeibergWitten geometries for nonsimply laced gauge groups.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.11638
 Bibcode:
 2021arXiv211011638B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 42 pages