Geometric unification of Higgs bundle vacua

Cvetič, Mirjam; Heckman, Jonathan J.; Rochais, Thomas B.; Torres, Ethan; Zoccarato, Gianluca

doi:10.1103/physrevd.102.106012

Cited by 10 publications

(15 citation statements)

References 65 publications

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“…In this paper we study 3d N = 1 vacua as obtained from M-theory on a local Spin (7) space. Such compactifications are closely related to 4d N = 1 vacua as obtained from Mtheory on local G 2 spaces, and F-theory on local elliptically fibered Calabi-Yau fourfolds, where holomorphic structures play a more prominent role [1,2]. These systems are also potentially of interest in the study of "4d N = 1/2" F-theory based models of dark energy (see e.g.…”

Section: Introductionmentioning

confidence: 95%

“…To frame the discussion to follow, recall that the local Spin(7) equations of motion amount to a hybrid of the Pantev-Wijnholt (PW) and Beasley-Heckman-Vafa (BHV) Higgs bundle systems [2], so we expect that the profile of localized zero modes will share some similarities with these cases. Starting from our local Spin(7) system on M 3 × S 1 for M 3 a three-manifold, we reach the PW system by assuming all fields are constant along the S 1 direction, and contracting Φ SD with the one-form on S 1 , and also dropping the contribution from the gauge field along the circle.…”

Section: Ultra-local Spin(7) Matter Fieldsmentioning

confidence: 99%

“…Anomalies of these symmetries, including mixed gravitational-parity and gauge-parity anomalies then provide non-perturbative control over some aspects of these systems. 2 The corresponding anomalies are often calculable, and provide us with a sharp tool in constraining the resulting 3d N = 1 vacua obtained from local Spin (7) spaces. More precisely, we shall be interested in the action of reflections for the 3d theory in a Euclidean spacetime: R 3d i : x i → −x i , and R 3d i : x j → x j for j = i.…”

Section: Introductionmentioning

confidence: 99%

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Reflections on the Matter of 3d $\mathcal{N} = 1$ Vacua and Local $Spin(7)$ Compactifications

Cvetič,

Heckman,

Torres

et al. 2021

Preprint

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We use Higgs bundles to study the 3d N = 1 vacua obtained from M-theory compactified on a local Spin(7) space given as a four-manifold M 4 of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. There can be strong quantum corrections to the massless degrees of freedom in the low energy effective field theory, but topologically robust quantities such as "parity" anomalies are still calculable. We show how geometric reflections of the compactification space descend to 3d reflections and discrete symmetries. The "parity" anomalies of the effective field theory descend from topological data of the compactification. The geometric perspective also allows us to track various perturbative and non-perturbative corrections to the 3d effective field theory. We also provide some explicit constructions of well-known 3d theories, including those which arise as edge modes of 4d topological insulators, and 3d N = 1 analogs of grand unified theories. An additional result of our analysis is that we are able to track the spectrum of extended objects and their transformations under higher-form symmetries.

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Section: Introductionmentioning

confidence: 95%

Section: Ultra-local Spin(7) Matter Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reflections on the Matter of 3d $\mathcal{N} = 1$ Vacua and Local $Spin(7)$ Compactifications

Cvetič,

Heckman,

Torres

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The simplest backgrounds to study the correspondence between non-perturbative effects in the 7d SYM, which originate from M2-brane instantons in M-theory, and generalized instantons of the colored SQM are abelian solutions to the BPS-equations with split spectral covers. These backgrounds have previously been studied in [21,[23][24][25]70] and serve as a precursor to studying abelian solutions to the BPS equations with non-split spectral covers. Configurations with split spectral covers already display many features relevant for model building.…”

Section: Jhep05(2021)002 5 Higgs Bundles With Split Spectral Coversmentioning

confidence: 99%

“…The class of G 2 -manifolds referred to as twisted connected sum G 2 -manifolds gives a landscape of roughly 10 6 compact geometries and have recently been studied, together with their singular limits, in the physics literature [15][16][17][18][19][20][21][22][23]. The gauge theory sector of these compactifications can be isolated and studied in local models of the geometry [21,24,25] using techniques involving Higgs bundles and spectral covers previously fruitful in F-theory model building [26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Jhep05(2021)002 1 Introductionmentioning

confidence: 99%

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

Hübner

2021

J. High Energ. Phys.

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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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Evidence for an algebra of G2 instantons

Zotto

Zhou

2022

J. High Energ. Phys.

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In this short note, we present some evidence towards the existence of an algebra of BPS G2 instantons. These are instantonic configurations that govern the partition functions of 7d SYM theories on local G2 holonomy manifolds $$ \mathcal{X} $$ X . To shed light on such structure, we begin investigating the relation with parent 4d $$ \mathcal{N} $$ N = 1 theories obtained by geometric engineering M-theory on $$ \mathcal{X} $$ X . The main point of this paper is to substantiate the following dream: the holomorphic sector of such theories on multi-centered Taub-NUT spaces gives rise to an algebra whose characters organise the G2 instanton partition function. As a first step towards this program we argue by string duality that a multitude of geometries $$ \mathcal{X} $$ X exist that are dual to well-known 4d SCFTs arising from D3 branes probes of CY cones: all these models are amenable to an analysis along the lines suggested by Dijkgraaf, Gukov, Neitzke and Vafa in the context of topological M-theory. Moreover, we discuss an interesting relation to Costello’s twisted M-theory, which arises at local patches, and is a key ingredient in identifying the relevant algebras.

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Geometric unification of Higgs bundle vacua

Cited by 10 publications

References 65 publications

Reflections on the Matter of 3d $\mathcal{N} = 1$ Vacua and Local $Spin(7)$ Compactifications

Reflections on the Matter of 3d $\mathcal{N} = 1$ Vacua and Local $Spin(7)$ Compactifications

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

Evidence for an algebra of G2 instantons

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