% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@PHDTHESIS{Bertle:626289,
      author       = {Bertle, Hanno},
      othercontributors = {Pomoni, Elli and Arutyunov, Gleb},
      title        = {{H}idden symmetries in four-dimensional $\mathcal{{N}} = 2$
                      superconformal gauge theories},
      school       = {University of Hamburg},
      type         = {Dissertation},
      reportid     = {PUBDB-2025-01364},
      pages        = {126},
      year         = {2025},
      note         = {Dissertation, University of Hamburg, 2025},
      abstract     = {The integrability properties of $\mathcal{N}=4$
                      Super-Yang-Mills in the planar limit have been studied
                      extensively and are well understood. For certain classes of
                      theories, obtained by orbifolding $\mathcal{N}=4$
                      Super-Yang-Mills, it was shown that planar integrability is
                      actually inherited and persists at the orbifold point.
                      However, to date, little is known for theories that are
                      deformed away from this fixed line in the marginal
                      couplings. The content of this thesis is the study of global
                      symmetries of the $\mathbb{Z}_2$-orbifold of $\mathcal{N}=4$
                      Super-Yang-Mills theory and its marginal deformations, with
                      the aim to investigate and describe hidden symmetries
                      appearing in this $\mathcal{N}=2$ superconformal field
                      theory. The process of orbifolding in order to obtain an
                      $\mathcal{N}=2$ theory appears to break the $\mathrm{SU}(4)$
                      R-symmetry down to $\mathrm{SU}(2)\times\mathrm{SU}(2)\times
                      \mathrm{U}(1)$. We are able to show that the previously
                      broken generators can actually be recovered by moving beyond
                      the Lie algebraic setting and adopting the notion of a Lie
                      algebroid. This remains true even away from the orbifold
                      point after performing a marginal deformation, where we
                      allow for independent variation of the
                      $\mathrm{SU}(N)\times\mathrm{SU}(N)$ gauge couplings.By
                      employing a Drinfeld-type twist of this $\mathrm{SU}(4)$ Lie
                      algebroid, we can capture this marginal deformation. The
                      resulting twist can be read off from the F- and D- terms of
                      the theory, and thus directly from the Lagrangian. Even
                      though at the orbifold point the algebraic structure is
                      associative, it becomes non-associative after the marginal
                      deformation. We explicitly check that the planar Lagrangian
                      of the theory is invariant under this twisted version of the
                      $\mathrm{SU}(4)$ algebroid, and we discuss implications of
                      this hidden symmetry for the spectrum of the $\mathcal{N}=2$
                      theory.},
      cin          = {UNI/TH},
      cid          = {$I:(DE-H253)UNI_TH-20120731$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611)},
      pid          = {G:(DE-HGF)POF4-611},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:gbv:18-ediss-125803},
      doi          = {10.3204/PUBDB-2025-01364},
      url          = {https://bib-pubdb1.desy.de/record/626289},
}