13 research outputs found
Contact Manifolds, Contact Instantons, and Twistor Geometry
Recently, Kallen and Zabzine computed the partition function of a twisted
supersymmetric Yang-Mills theory on the five-dimensional sphere using
localisation techniques. Key to their construction is a five-dimensional
generalisation of the instanton equation to which they refer as the contact
instanton equation. Subject of this article is the twistor construction of this
equation when formulated on K-contact manifolds and the discussion of its
integrability properties. We also present certain extensions to higher
dimensions and supersymmetric generalisations.Comment: v3: 28 pages, clarifications and references added, version to appear
in JHE
Plu"cker embedding of the Hilbert Space grassmannian and boson-fermion correspondence via coherent states
In this note we give a Pluecker type description of the image of the embedding of the Hilbert space grassmannian of Segal and Wilson,
obtained by resorting to the theory of quasi-free states of the CAR algebras. We also derive a boson-fermion correspondence via diastatic identities and coherent states
PlĂĽcker Embedding of the Hilbert Space Grassmannian and Boson-Fermion Correspondence via Coherent States
On Some Geometric Aspects of Coherent States
In this note we review some issues in the geometrical approach to coherent states (CS). Specifically, we reformulate the standard (compact, simple) Lie group CS by placing them within the frameworks of geometric quantum mechanics and holomorphic geometric quantization and establishing a connection with Fisher information theory. Secondly, we briefly revisit the CS-approach to the Hilbert space Grassmannian and the KP- hierarchy and finally we discuss the CS aspects emerging in the geometric approach to Landau levels via the Fourier-Mukai-Nahm transform