Extended supersymmetric \(\sigma \)-model based on the \(SO(2N+1)\) Lie algebra of the fermion operators

DOI10.1016/j.nuclphysb.2008.05.008zbMath1189.81137arXiv0712.4208OpenAlexW2052083446MaRDI QIDQ978523

Flávio Cordeiro, Constança Providência, Seiya Nishiyama, João da Providência

Publication date: 25 June 2010

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.4208

zbMATH Keywords

Killing potentialBogoliubov transformation

Mathematics Subject Classification ID

Model quantum field theories (81T10) Supersymmetric field theories in quantum mechanics (81T60) Applications of Lie groups to the sciences; explicit representations (22E70) Kähler manifolds (32Q15) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items (6)

A NEW DESCRIPTION OF MOTION OF THE FERMIONIC SO(2N+2) TOP IN THE CLASSICAL LIMIT UNDER THE QUASI-ANTICOMMUTATION RELATION APPROXIMATION ⋮ Anomaly-free supersymmetric \(\frac{{{\text{SO}}\left( {2N + 2} \right)}}{{{\text{U}}\left( {N + 1} \right)}} \) {\(\sigma\)}-model based on the SO(2\(N\) + 1) Lie algebra of the fermion operators ⋮ Nonlinear Bogolyubov-Valatin transformations: two modes ⋮ Modified non-Euclidean transformation on the SO(2N+2) U(N+1) Grassmannian and SO(2N + 1) random phase approximation for unified description of Bose and Fermi type collective excitations ⋮ Mean-field theory based on the Jacobi hsp ≔ semidirect sum hN⋊sp(2N,R)C algebra of boson operators ⋮ $\frac{{\rm SO}(2N)}{U(N)}$ Riccati–Hartree–Bogoliubov equation based on the SO(2N) Lie algebra of the fermion operators

Cites Work

• Unnamed Item
• Hyperkähler metrics and supersymmetry
• Construction and analysis of anomaly-free supersymmetric SO(2N)/U(N) \(\sigma\)-models
• Manifest supersymmetry for BPS walls in \(N=2\) nonlinear sigma models
• The Group Theoretical Structure of Fermion Many-Body Systems Arising from the Canonical Anticommutation Relation. I: Lie Algebras of Fermion Operators and Exact Generator Coordinate Representations of State Vectors
• Time Dependent SO(2N+1) Theory for Unified Description of Bose and Fermi Type Collective Excitations
• Kahler Normal Coordinate Expansion in Supersymmetric Theories
• Ricci-flat Kähler manifolds from supersymmetric gauge theories

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