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@ARTICLE{Longhi:434661,
      author       = {Longhi, Pietro and Nieri, Fabrizio and Pittelli, Antonio},
      title        = {{L}ocalization of 4d $\mathcal{{N}}=1$ theories on
                      $\mathbb{{D}}^2\times \mathbb{{T}}^2$},
      journal      = {Journal of high energy physics},
      volume       = {1912},
      issn         = {1029-8479},
      address      = {[Trieste]},
      publisher    = {SISSA},
      reportid     = {PUBDB-2020-00222, arXiv:1906.02051. DESY-19-214},
      pages        = {147},
      year         = {2019},
      note         = {68 pages including appendices},
      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.},
      keywords     = {supersymmetry: transformation (INSPIRE) / multiplet: chiral
                      (INSPIRE) / space: compact (INSPIRE) / boundary condition
                      (INSPIRE) / partition function (INSPIRE) / localization
                      (INSPIRE) / gauge field theory (INSPIRE) / holomorphic
                      (INSPIRE) / cohomology (INSPIRE) / R symmetry (INSPIRE) /
                      topology (INSPIRE) / torus (INSPIRE)},
      cin          = {T},
      ddc          = {530},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF3-611)},
      pid          = {G:(DE-HGF)POF3-611},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {1906.02051},
      howpublished = {arXiv:1906.02051},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1906.02051;\%\%$},
      UT           = {WOS:000504963100001},
      doi          = {10.1007/JHEP12(2019)147},
      url          = {https://bib-pubdb1.desy.de/record/434661},
}