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Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces

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Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces. / McBreen, Michael Ben; Sheshmani, Artan; Yau, Shing-Tung.

ArXiv, 2020.

Publikation: Working paper/Preprint Working paperForskning

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McBreen, Michael Ben, Artan Sheshmani og Shing-Tung Yau Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces. ArXiv. 2020., 46 s.

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McBreen, Michael Ben ; Sheshmani, Artan ; Yau, Shing-Tung. / Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces. ArXiv, 2020.

Bibtex

@techreport{ecc0d4eba3ca4e2caa6fd663e77fe940,
title = "Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces",
abstract = "We study moduli spaces of twisted quasimaps to a hypertoric variety X, arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametrise general quiver representations whose building blocks are maps between rank one sheaves on ℙ1, subject to a stability condition, associated to the quiver, involving both the sheaves and the maps. We show that the singular cohomology of these moduli spaces is naturally identified with the Ext group of a pair of holonomic modules over the `quantized loop space' of X, which we view as a Higgs branch for a related theory with infinitely many matter fields. We construct the coulomb branch of this theory, and find that it is a periodic analogue of the coulomb branch associated to X. Using the formalism of symplectic duality, we derive an expression for the generating function of twisted quasimap invariants in terms of the character of a certain tilting module on the periodic coulomb branch. We give a closed formula for this generating function when X arises as the abelianisation of the N-step flag quiver.",
author = "McBreen, {Michael Ben} and Artan Sheshmani and Shing-Tung Yau",
year = "2020",
month = may,
language = "English",
publisher = "ArXiv",
type = "WorkingPaper",
institution = "ArXiv",

}

RIS

TY - UNPB

T1 - Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces

AU - McBreen, Michael Ben

AU - Sheshmani, Artan

AU - Yau, Shing-Tung

PY - 2020/5

Y1 - 2020/5

N2 - We study moduli spaces of twisted quasimaps to a hypertoric variety X, arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametrise general quiver representations whose building blocks are maps between rank one sheaves on ℙ1, subject to a stability condition, associated to the quiver, involving both the sheaves and the maps. We show that the singular cohomology of these moduli spaces is naturally identified with the Ext group of a pair of holonomic modules over the `quantized loop space' of X, which we view as a Higgs branch for a related theory with infinitely many matter fields. We construct the coulomb branch of this theory, and find that it is a periodic analogue of the coulomb branch associated to X. Using the formalism of symplectic duality, we derive an expression for the generating function of twisted quasimap invariants in terms of the character of a certain tilting module on the periodic coulomb branch. We give a closed formula for this generating function when X arises as the abelianisation of the N-step flag quiver.

AB - We study moduli spaces of twisted quasimaps to a hypertoric variety X, arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametrise general quiver representations whose building blocks are maps between rank one sheaves on ℙ1, subject to a stability condition, associated to the quiver, involving both the sheaves and the maps. We show that the singular cohomology of these moduli spaces is naturally identified with the Ext group of a pair of holonomic modules over the `quantized loop space' of X, which we view as a Higgs branch for a related theory with infinitely many matter fields. We construct the coulomb branch of this theory, and find that it is a periodic analogue of the coulomb branch associated to X. Using the formalism of symplectic duality, we derive an expression for the generating function of twisted quasimap invariants in terms of the character of a certain tilting module on the periodic coulomb branch. We give a closed formula for this generating function when X arises as the abelianisation of the N-step flag quiver.

M3 - Working paper

BT - Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces

PB - ArXiv

ER -