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Deformations of G2-Structures, Strin...

Barbosa, Rodrigo de Menezes.

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Deformations of G2-Structures, String Dualities and Flat Higgs Bundles.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Deformations of G2-Structures, String Dualities and Flat Higgs Bundles./
Author:	Barbosa, Rodrigo de Menezes.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	178 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Contained By:	Dissertations Abstracts International81-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13877751
ISBN:	9781085587518

Deformations of G2-Structures, String Dualities and Flat Higgs Bundles.
Barbosa, Rodrigo de Menezes.

Deformations of G2-Structures, String Dualities and Flat Higgs Bundles. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 178 p.

Source: Dissertations Abstracts International, Volume: 81-02, Section: B.

Thesis (Ph.D.)--University of Pennsylvania, 2019.

This item must not be sold to any third party vendors.

We study M-theory compactifications on G2-orbifolds and their resolutions given by total spaces of coassociative ALE-fibrations over a compact flat Riemannian 3-manifold Q. The flatness condition allows an explicit description of the deformation space of closed G2-structures, and hence also the moduli space of supersymmetric vacua: it is modeled by flat sections of a bundle of Brieskorn-Grothendieck resolutions over Q. Moreover, when instanton corrections are neglected, we obtain an explicit description of the moduli space for the dual type IIA string compactification. The two moduli spaces are shown to be isomorphic for an important example involving A1-singularities, and the result is conjectured to hold in generality. We also discuss an interpretation of the IIA moduli space in terms of "flat Higgs bundles" on Q and explain how it suggests a new approach to SYZ mirror symmetry, while also providing a description of G2-structures in terms of B-branes. The net result is two algebro-geometric descriptions of the moduli space of complexified G2-structures: one as a character variety and a mirror description in terms of a Hilbert scheme of points. Usual G2-deformations are parametrized by spectral covers of flat Higgs bundles.We also discuss a few ongoing developments: (1) we propose a heterotic dual to our main example, (2) we explain how the moduli space of flat Higgs bundles fits into a family of moduli spaces of extended Bogomolnyi monopoles, and (3) we introduce a natural variation of Hodge structures over the complexified G2-moduli space, and conjecture this space admits the structure of a complex integrable system.

ISBN: 9781085587518Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Deformation theory

Deformations of G2-Structures, String Dualities and Flat Higgs Bundles.
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100 1 $a Barbosa, Rodrigo de Menezes. $3 3549949
245 1 0 $a Deformations of G2-Structures, String Dualities and Flat Higgs Bundles.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 178 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
500 $a Advisor: Pantev, Tony G.
502 $a Thesis (Ph.D.)--University of Pennsylvania, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a We study M-theory compactifications on G2-orbifolds and their resolutions given by total spaces of coassociative ALE-fibrations over a compact flat Riemannian 3-manifold Q. The flatness condition allows an explicit description of the deformation space of closed G2-structures, and hence also the moduli space of supersymmetric vacua: it is modeled by flat sections of a bundle of Brieskorn-Grothendieck resolutions over Q. Moreover, when instanton corrections are neglected, we obtain an explicit description of the moduli space for the dual type IIA string compactification. The two moduli spaces are shown to be isomorphic for an important example involving A1-singularities, and the result is conjectured to hold in generality. We also discuss an interpretation of the IIA moduli space in terms of "flat Higgs bundles" on Q and explain how it suggests a new approach to SYZ mirror symmetry, while also providing a description of G2-structures in terms of B-branes. The net result is two algebro-geometric descriptions of the moduli space of complexified G2-structures: one as a character variety and a mirror description in terms of a Hilbert scheme of points. Usual G2-deformations are parametrized by spectral covers of flat Higgs bundles.We also discuss a few ongoing developments: (1) we propose a heterotic dual to our main example, (2) we explain how the moduli space of flat Higgs bundles fits into a family of moduli spaces of extended Bogomolnyi monopoles, and (3) we introduce a natural variation of Hodge structures over the complexified G2-moduli space, and conjecture this space admits the structure of a complex integrable system.
590 $a School code: 0175.
650 4 $a Mathematics. $3 515831
650 4 $a Quantum physics. $3 726746
653 $a Deformation theory
653 $a G2-Manifolds
653 $a Higgs bundles
653 $a Mirror symmetry
653 $a Moduli spaces
653 $a M-Theory
690 $a 0405
690 $a 0599
710 2 $a University of Pennsylvania. $b Mathematics. $3 2101086
773 0 $t Dissertations Abstracts International $g 81-02B.
790 $a 0175
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13877751