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@PHDTHESIS{Mansi:628058,
      author       = {Mansi, Lorenzo},
      othercontributors = {Lawrie, Craig},
      title        = {{T}he {H}iggs {B}ranch of {S}ix {D}imensional
                      {S}upersymmetric {T}heories: {M}agnetic {Q}uivers,
                      {G}eometry, and {H}asse {D}iagrams},
      school       = {Universität Hamburg},
      type         = {Dissertation},
      address      = {Hamburg},
      publisher    = {Verlag Deutsches Elektronen-Synchrotron DESY},
      reportid     = {PUBDB-2025-01709, DESY-THESIS-2025-010},
      series       = {DESY-THESIS},
      pages        = {217},
      year         = {2025},
      note         = {Dissertation, Universität Hamburg, 2025},
      abstract     = {In this thesis, we report recent advancements in the
                      understanding of Higgs branch moduli spacesof
                      six-dimensional (1,0) supersymmetric quantum field theories,
                      along with related developments.These progresses have been
                      achieved by exploiting the interplay between geometrical
                      engineeringand techniques in quiver gauge theories, leading
                      to new insights into the Higgs mechanism’s actionin
                      higher-dimensional supersymmetric theories.Paper I: We
                      present an extension of the magnetic quiver technique to a
                      class of non-gravitationalsupersymmetric quantum field
                      theories in six dimensions known as Little String Theories
                      (LSTs).These theories also exhibit a higher-group symmetry
                      structure. Notably, we prove a monotonicitytheorem
                      describing the evolution of κR, a quantity characterizing
                      the higher group symmetry, underpartial Higgsing
                      patterns.Paper II: Specializing to a brane engineering
                      framework, we construct a family of LST modelswith a natural
                      interpretation as an F-theory compactification. We derive
                      the magnetic quiver forits Higgs branch moduli space and
                      study the partial Higgsing pattern using the quiver
                      subtractiontechnique. By leveraging the alternative
                      description of Higgsing as a complex structure
                      deformationwithin the F-theory geometric realization, we
                      establish for the first time a concrete link
                      betweengeometric approaches and algorithm-based predictions
                      from quiver gauge theories.Paper III: Building upon the
                      geometric connections established in the previous paper, we
                      considera class of six-dimensional Super Conformal Field
                      Theories (SCFTs) engineered through
                      F-theorycompactifications and analyze their partial Higgsing
                      patterns. Additionally, we provide a braneconstruction in
                      Type IIA featuring an exotic orbifold for this class, from
                      which we extract themagnetic quiver. We then propose a
                      tentative, case-specific quiver algorithm that successfully
                      eproduces the geometric results.Paper IV: We formalize a
                      quiver algorithm designed to predict the partial Higgsing
                      patterns onthe Coulomb branch of three-dimensional N= 4
                      quiver gauge theories with special orthogonal andsymplectic
                      gauge groups. The algorithm is benchmarked against
                      predictions derived from geometricconsiderations in the
                      context of Class S theories and F-theory engineering of
                      six-dimensional SCFTs.},
      cin          = {T},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / DFG
                      project G:(GEPRIS)390833306 - EXC 2121: Quantum Universe
                      (390833306) / DFG project G:(GEPRIS)506632645 - SFB 1624:
                      Höhere Strukturen, Modulräume und Integrabilität
                      (506632645)},
      pid          = {G:(DE-HGF)POF4-611 / G:(GEPRIS)390833306 /
                      G:(GEPRIS)506632645},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
      doi          = {10.3204/PUBDB-2025-01709},
      url          = {https://bib-pubdb1.desy.de/record/628058},
}