A simple introduction to Gröbner basis methods in string phenomenology

DOI10.1155/2011/217035zbMath1234.81112arXiv0901.1662OpenAlexW3103654562WikidataQ58655095 ScholiaQ58655095MaRDI QIDQ765434

James A. Gray

Publication date: 19 March 2012

Published in: Advances in High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.1662

Mathematics Subject Classification ID

Unified quantum theories (81V22) Supersymmetric field theories in quantum mechanics (81T60) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Software, source code, etc. for problems pertaining to quantum theory (81-04)

Related Items

Exploring the potential energy landscape over a large parameter-space, Testing R-parity with geometry, Tensor product of evolution algebras, Stabilizing the complex structure in heterotic Calabi-Yau vacua, Yukawa textures from heterotic stability walls, The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications, Parallel degree computation for binomial systems, Complete intersection moduli spaces in \(\mathcal{N} = 4\) gauge theories in three dimensions, Heterotic line bundle standard models, Numerical algebraic geometry: a new perspective on gauge and string theories, Numerical elimination and moduli space of vacua, Jumping spectra and vanishing couplings in heterotic line bundle standard models, Chern-Simons: Fano and Calabi-Yau, Numerical polynomial homotopy continuation method and string vacua, The geometry of generations, Veronese geometry and the electroweak vacuum moduli space

Uses Software

• Macaulay2
• SINGULAR
• STRINGVACUA

Cites Work

• On the geometry of super Yang-Mills theories: phases and irreducible polynomials
• Counting gauge invariant operators in SQCD with classical gauge groups
• Non-geometric flux vacua, S-duality and algebraic geometry
• Counting BPS operators in gauge theories: quivers, syzygies and plethystics
• STRINGVACUA. A Mathematica package for studying vacuum configurations in string phenomenology
• Localization and primary decomposition of polynomial ideals
• Vacuum geometry and the search for new physics
• Exploring the vacuum geometry of \(\mathcal N=1\) gauge theories
• Algebras and non-geometric flux vacua
• Mastering the master space
• Gröbner bases and primary decomposition of polynomial ideals
• Direct methods for primary decomposition
• The Hilbert series of adjoint SQCD
• Gauge Coupling Unification and Light Exotica in String Theory
• On the existence of non-supersymmetric black hole attractors for two-parameter Calabi-Yau's and attractor equations
• New Calabi‐Yau manifolds with small Hodge numbers
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