Graded Hopf Maps and Fuzzy Superspheres

Abstract

We argue supersymmetric generalizations of fuzzy two- and four-spheres based on the unitary-orthosymplectic algebras, $uosp(N|2)$ and $uosp(N|4)$, respectively. Supersymmetric version of Schwinger construction is applied to derive graded fully symmetric representation for fuzzy superspheres. As a classical counterpart of fuzzy superspheres, graded versions of 1st and 2nd Hopf maps are introduced, and their basic geometrical structures are studied. It is shown that fuzzy superspheres are represented as a "superposition" of fuzzy superspheres with lower supersymmetries. We also investigate algebraic structures of fuzzy two- and four-superspheres to identify $su(2|N)$ and $su(4|N)$ as their enhanced algebraic structures, respectively. Evaluation of correlation functions manifests such enhanced structure as quantum fluctuations of fuzzy supersphere.

56 pages, no figures, two tables, references added, minor corrections, to appear in NPB

References in corpus (11)

• A Gravity Theory on Noncommutative Spaces
• OSp(4|2) Superconformal Mechanics
• Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Second Hopf map and supersymmetric mechanics with Yang monopole
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
• N=4, 3D Supersymmetric Quantum Mechanics in Non-Abelian Monopole Background
• Matrix models and the gravitational interaction
• Generalized Berezin-Toeplitz quantization of Kaehler supermanifolds
• Construction of Fuzzy Spaces and Their Applications to Matrix Models

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• Tsirelson's bound and supersymmetric entangled states
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• Super quantum Dirac operator on the q-deformed super fuzzy sphere in instanton sector using quantum super Ginsparg-Wilson algebra
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Deformation of Matrix Geometry via Landau Level Evolution