Seminar “Modern Mathematical Physics”

Date and Time: Tuesday, 1 December 2020, at 1:00 PM

Venue: Online conference in Zoom, Bogoliubov Laboratory of Theoretical Physics

Seminar topic: «New approach to N=2 supersymmetric Ruijsenaars-Schneider model»

Speaker: Nikolay Kozyrev

Abstract:

Ruijsenaars-Shchneider model is one of the best-known integrable systems. It can be considered as a relativistic generalization of the Calogero-Moser model. Like the Calogero-Moser system, interaction in this model depends on differences of coordinates of pairs of particles 𝑥_𝑖 − 𝑥_𝑗 and is given by the Weierstrass elliptic function, which, with a specific choice of parameters, can be reduced to a rational function or inverse of sine/tangent. The last case is most interesting, as in the rational case the model can be reduced to the free one after some simple coordinate transformation. Despite the simplicity of the model, the construction of its supersymmetric generalization is not so easy due to arbitrariness in the choice of the bosonic Hamiltonian, which reproduces the equations of motion. One of N=2 generalizations was constructed in [Phys.Lett.B 807 (2020) 135545], where the usual free Hamiltonian with modified Dirac brackets was used, and it was possible to achieve N=2 supersymmetry for the arbitrary potential. We consider a different approach, which involves standard Dirac brackets for the fermions, but uses supercharges with more complicated structure. In this case, the nontrivial condition on the function that describes the interaction appears, which fixes the function as rational or trigonometric/hyperbolic cotangent, which are required to ensure integrability of the model. Systems, which can be constructed this way, are shown to be equivalent to ones found in [Phys.Lett.B 807 (2020) 135545] with some modification of the fermionic terms.