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

Longhi, Pietro; Nieri, Fabrizio; Pittelli, Antonio

doi:10.1007/JHEP12(2019)147

Journal Article

PUBDB-2020-00222

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

Longhi, P. ; Nieri, F. (Corresponding author)DESY* ; Pittelli, A.

2019
SISSA [Trieste]

Journal of high energy physics 1912, 147 (2019) [10.1007/JHEP12(2019)147]

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Please use a persistent id in citations: doi:10.1007/JHEP12(2019)147 doi:10.3204/PUBDB-2020-00222

Report No.: DESY-19-214; arXiv:1906.02051

Abstract: 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.

Keyword(s): supersymmetry: transformation ; multiplet: chiral ; space: compact ; boundary condition ; partition function ; localization ; gauge field theory ; holomorphic ; cohomology ; R symmetry ; topology ; torus

Classification:

ddc:530

Note: 68 pages including appendices

Contributing Institute(s):

Theorie-Gruppe (T)

Research Program(s):

611 - Fundamental Particles and Forces (POF3-611) (POF3-611)

Experiment(s):

No specific instrument

Appears in the scientific report 2019

Database coverage:
Creative Commons Attribution CC BY 4.0

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