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Mirror symmetry with branes by equivariant Verlinde formulae

Hausel, Tamas and Mellit, Anton and Pei, Du (2017) Mirror symmetry with branes by equivariant Verlinde formulae. . (Submitted)

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We find an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL(2) Higgs moduli space on a Riemann surface. On one side we have the components of the Lagrangian brane of U(1,1) Higgs bundles whose mirror was proposed by Nigel Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL(2) Higgs moduli space. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin's proposal.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Pei, Du0000-0001-5587-6905
Additional Information:We would like to thank Sergei Gukov and Paul Harmsen for encouragement and their interest in this paper, Jørgen E. Andersen, Andr ´as Szenes, Laura Schaposnik, Nigel Hitchin, Penghui Li, Iordan Ganev and the referee for useful explanations and comments. The research in this paper was supported by an Advanced Grant “Arithmetic and physics of Higgs moduli spaces” no. 320593 of the European Research Council, the NCCR SwissMAP of the Swiss National Foundation, START-Project Y963-N35 of the Austrian Science Fund (FWF) , the center of excellence grant “Center for Quantum Geometry of Moduli Space” from the Danish National Research Foundation (DNRF95), by the Walter Burke Institute for Theoretical Physics, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In particular, the idea of the computation in this paper arose during the ”Retreat on Higgs bundles, real groups, Langlands duality and mirror symmetry” in the Bernoulli center at EPF Lausanne in January 2016.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)320593
Swiss National Science Foundation (SNSF)UNSPECIFIED
FWF Der WissenschaftsfondsY963-N35
Danish National Research FoundationDNRF95
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
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Record Number:CaltechAUTHORS:20171214-111513089
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83923
Deposited By: Joy Painter
Deposited On:14 Dec 2017 19:36
Last Modified:02 Jun 2023 00:37

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