Brini, A. orcid.org/0000-0002-3758-827X and van Gemst, K. (Submitted: 2021) Mirror symmetry for extended affine Weyl groups. arXiv. (Submitted)
Abstract
We give a uniform, Lie-theoretic mirror symmetry construction for the Frobenius manifolds defined by Dubrovin--Zhang in arXiv:hep-th/9611200 (https://arxiv.org/abs/hep-th/9611200) on the orbit spaces of extended affine Weyl groups, including exceptional Dynkin types. The B-model mirror is given by a one-dimensional Landau--Ginzburg superpotential constructed from a suitable degeneration of the family of spectral curves of the affine relativistic Toda chain for the corresponding affine Poisson--Lie group. As applications of our mirror theorem we give closed-form expressions for the flat coordinates of the Saito metric and the Frobenius prepotentials in all Dynkin types, compute the topological degree of the Lyashko--Looijenga mapping for certain higher genus Hurwitz space strata, and construct hydrodynamic bihamiltonian hierarchies (in both Lax--Sato and Hamiltonian form) that are root-theoretic generalisations of the long-wave limit of the extended Toda hierarchy.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Authors. For re-use permissions please contact the authors. |
Keywords: | math.AG; math.AG; hep-th; math-ph; math.MP; nlin.SI |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Science Research Council EP/S003657/2 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 25 May 2021 07:39 |
Last Modified: | 25 May 2021 07:39 |
Published Version: | https://arxiv.org/abs/2103.12673v1 |
Status: | Submitted |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:174449 |