Supersymmetry in Integrable Systems
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".
Deadline for manuscript submissions: closed (30 June 2020) | Viewed by 2783
Special Issue Editor
Special Issue Information
Dear Colleagues,
It is well known that symmetries play a central role in modern mathematical physics. In the classical domain, they are indispensable for constructing explicit solutions to equations of motion. Celebrated applications vary from the Kepler problem to the geodesic motion in black hole spacetime. In quantum theory, they facilitate the construction of eigenstates of the Hamiltonian by purely algebraic means, the Calogero model being a classical example.
A system is integrable if it possesses as many integrals of motion as the number of degrees of freedom. If there are extra integrals over and above those, it is superintegrable. Extensive studies of models with abundant symmetries over the last forty years paved the way for a separate ramification of modern mathematical physics entitled Integrable Systems.
The rational Calogero model, describing one-dimensional particles with inverse-square pairwise interactions, plays a significant role in mathematical and theoretical physics. Being the prime example of an integrable and solvable many-body system, it appears in many areas of modern mathematical physics, from high-energy to condensed-matter physics. An intriguing hypothesis suggests that the large-N limit of the n-particle N=4 superconformal rational Calogero model provides a microscopic description of the extremal Reissner-Nordstrom black hole in the near-horizon limit. Since then, the task of constructing an (at least) N=4 supersymmetric n-particle rational Calogero model has been the subject of a number of papers, but with only partial success. Despite the simplicity of the Calogero Hamiltonian, the attempts to find an N=4 supersymmetric version beyond the four-particle case were unsuccessful. In contrast, the N=2 supersymmetric Calogero model was found many years ago.
This Special Issue of Symmetry features articles about Supersymmetric Integrable systems, with supersymmetry and/or integrability as the unifying theme. We are soliciting contributions covering a broad range of topics including the following: symmetries of bosonic integrable systems; relations between the geometry and integrability; supersymmetric extensions of the integrable systems; integrable systems that possess additional symmetries such as conformal symmetry or/and extended supersymmetry; the superspace description of the integrable models with N =2 and N =4 supersymmetry; the Ricci-flat geometries invariant under the Schrödinger group and integrable geodesic motion on such spacetimes; the near-horizon limits for non-singular black-hole geometries and integrable geodesic motion on such spacetimes; the N =4 superconformal dynamics of a particle on the different near-horizon extreme black-hole backgrounds.
Prof. Sergey Krivonos
Guest Editor
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Keywords
- integrable systems
- (nonrelativistic) conformal groups
- geometries enjoying conformal isometry group
- hidden symmetries of spacetime
- extended supersymmetry
- superconformal mechanics
- Calogero models
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