7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds

Iakovidis, Nikolaos; Qiu, Jian; Rocén, Andreas; Zabzine, Maxim

doi:10.1007/jhep06(2020)026

Cited by 12 publications

(11 citation statements)

References 25 publications

(75 reference statements)

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“…4d [25,32,[36][37][38][39], 5d [40][41][42][43][44], and 7d [45][46][47]. We refer to [31] and to references therein for an exhaustive bibliography.…”

Section: Summary Of Resultsmentioning

confidence: 99%

Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter

Festuccia,

Gorantis,

Pittelli

et al. 2020

Preprint

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We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun's theory on S 4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

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“…4d [25,32,[36][37][38][39], 5d [40][41][42][43][44], and 7d [45][46][47]. We refer to [31] and to references therein for an exhaustive bibliography.…”

Section: Summary Of Resultsmentioning

confidence: 99%

Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter

Festuccia,

Gorantis,

Pittelli

et al. 2020

Preprint

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“…If one stacks these pictures together according to the power of u, one gets a 3D cone and the multiplicity is controlled by the distance of a lattice point to the boundary of the cone. For more examples, including singular HK varieties, see [IQRZ20]. We will plot the cohomology of O(1) and O(2), their higher cohomology vanishes too.…”

Section: J Qiumentioning

confidence: 99%

Rozansky–Witten Theory, Localised Then Tilted

Qiu

2022

Commun. Math. Phys.

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The paper has two parts, in the first part, we apply the localisation technique to the Rozansky–Witten theory on compact hyperkähler targets. We do so via first reformulating the theory as some supersymmetric sigma-model. We obtain the exact formula for the partition function with Wilson loops on $$S^1\times \Sigma _g$$ S 1 × Σ g and the lens spaces, the results match with earlier computations using Feynman diagrams on K3. The second part is motivated by a very curious paper (Gukov in J Geom Phys 168, 104311, 2021), where the equivariant index formula for the dimension of the Hilbert space of the Rozansky–Witten theory is interpreted as a kind of Verlinde formula. In this interpretation, the fixed points of the target hyperkähler geometry correspond to certain ‘states’. We extend the formalism of part one to incorporate equivariance on the target geometry. For certain non-compact hyperkähler geometry, we can apply the tilting theory to the derived category of coherent sheaves, whose objects label the Wilson loops, allowing us to pick a basis for the latter. We can then compute the fusion products in this basis and we show that the objects that have diagonal fusion rules are intimately related to the fixed points of the geometry. Using these objects as basis to compute the dimension of the Hilbert space leads back to the Verlinde formula, thus answering the question that motivated the paper.

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“…Several results about this theory on curved spaces have been obtained recently, see e.g. [55][56][57], working à la Festuccia-Seiberg [58], however a detailed study of the case of pure G 2 holonomy is complicated by the fact that in this latter case one has only a single parallel spinor, and therefore the localising locus is not reduced to a combination of fixed points arising from a Reeb-like structure. Nevertheless, twisted versions of this theory are well-known to exist and lead to an interesting cohomological field theory depending on the G 2 structure of X -see [59][60][61].…”

Section: Localising On G 2 Instantonsmentioning

confidence: 99%

Evidence for an Algebra of $\boldsymbol{G_2}$ Instantons

Del Zotto,

Oh,

Zhou

2021

Preprint

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In this short note, we present some evidence towards the existence of an algebra of BPS G 2 instantons. These are instantonic configurations that govern the partition functions of 7d SYM theories on local G 2 holonomy manifolds X . To shed light on such structure, we begin investigating the relation with parent 4d N = 1 theories obtained by geometric engineering M-theory on 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 G 2 instanton partition function. As a first step towards this program we argue by string duality that a multitude of geometries 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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7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds

Cited by 12 publications

References 25 publications

Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter

Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter

Rozansky–Witten Theory, Localised Then Tilted

Evidence for an Algebra of $\boldsymbol{G_2}$ Instantons

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