Generalizations of parabolic Higgs bundles, real structures, and integrability

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

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Torelli theorem for the moduli space of symplectic parabolic Higgs bundles

Bulletin des Sciences Mathématiques ◽

10.1016/j.bulsci.2021.102978 ◽

2021 ◽

pp. 102978

Author(s):

Sumit Roy

Keyword(s):

Moduli Space ◽

Higgs Bundles ◽

Torelli Theorem

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Local G2-manifolds, Higgs bundles and a colored quantum mechanics

Journal of High Energy Physics ◽

10.1007/jhep05(2021)002 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Max Hübner

Keyword(s):

Quantum Mechanics ◽

Gauge Theories ◽

Supersymmetric Quantum Mechanics ◽

Higgs Bundle ◽

Higgs Bundles ◽

View Point ◽

Yang Mills ◽

G2 Manifolds ◽

Supersymmetric Gauge ◽

M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

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