Fakulta matematiky, fyziky
a informatiky
Univerzita Komenského v Bratislave

Seminár Katedry teoretickej fyziky - Eugenia Boffo (7.5.2024)

v utorok 7.5.2024 o 14:00 hod. v miestnosti F2/125

01. 05. 2024 22.06 hod.
Od: Peter Maták

Prednášajúci: Eugenia Boffo 

Názov: On the N=2 spinning particle

Termín: 7.5.2024, 14:00 hod., miestnosť F2 125

The spinning particle, which is a relativistic massless particle with a supersymmetric worldline, is the particle analogue of the Ramond-Neveu-Schwarz superstring. As such, it can serve as a playground for the understanding of second quantized string theory. Within the context of Becchi-Rouet-Stora-Tyutin cohomological techniques, different sectors arise for the representation of the bosonic ghosts associated with supersymmetry, and are distinguished by different picture numbers. After explaining some basics of differential geometry of supermanifolds, I will discuss BRST cohomology, which emerges also from the Poincare'-Hilbert series (besides just from direct computation). Such series is a very convenient means to compute the partition function and extract various kinds of information. For the case under inspection, the specific results will be highlighted.
Next I will turn to the second quantization of the spinning particle, which yields a (gauge) field theory. BRST can only reproduce the classical free BV theory, and leaves one to wonder whether it would be possible to get the interactions too. After all, homotopy Lie algebras are known to help in this regard. Moreover, in open string field theory the interactions have already been constructed thanks to the work of Witten (Phys. Rev. D 46, 5467 (1992)). In the case of a spinning particle, I will discuss the necessity of a different approach, that relies instead on the existence of a convenient deformation of the BRST operator by fields. All concepts shall be sufficiently defined and explained.