Home > Publications database > Localization of 4d $\mathcal{N}=1$ theories on $\mathbb{D}^2\times \mathbb{T}^2$ > print

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005     20250729163303.0
024 7 _ |a Longhi:2019hdh
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024 7 _ |a arXiv:1906.02051
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024 7 _ |a 10.1007/JHEP12(2019)147
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088 1 _ |a arXiv:1906.02051
100 1 _ |a Longhi, Pietro
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245 _ _ |a Localization of 4d $\mathcal{N}=1$ theories on $\mathbb{D}^2\times \mathbb{T}^2$
260 _ _ |a [Trieste]
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336 7 _ |a Journal Article
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500 _ _ |a 68 pages including appendices
520 _ _ |a We consider 4d $ \mathcal{N} $ = 1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d $ \mathcal{N} $ = 1 degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.
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650 _ 7 |a supersymmetry: transformation
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650 _ 7 |a multiplet: chiral
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650 _ 7 |a space: compact
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650 _ 7 |a boundary condition
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650 _ 7 |a partition function
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650 _ 7 |a localization
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650 _ 7 |a gauge field theory
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650 _ 7 |a holomorphic
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650 _ 7 |a cohomology
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650 _ 7 |a R symmetry
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650 _ 7 |a topology
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650 _ 7 |a torus
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700 1 _ |a Nieri, Fabrizio
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700 1 _ |a Pittelli, Antonio
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773 _ _ |a 10.1007/JHEP12(2019)147
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787 0 _ |a Longhi, Pietro et.al.
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|t Localization of 4d $\mathcal{N} = 1$ theories on $\mathbb{D}^2 \times \mathbb{T}^2$
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