Baxter Q-operators and supersymmetric gauge theories

• Applicant: Dr. Rouven Frassek
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2019 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 416527151

• Final Report Year: 2021

Final Report Abstract

The fellowship has let to several interesting results. We revealed some of the structure of the QQ-system for spin chains beyond A-type and understood what the main differences are compared to D-type. The QQ-system obtained is ready to be used for the Fishnet CFT and also ready to be adapted to ABJM Chern-Simons theory. We have learned that for the full understanding of the QQ-system the results for Lie algebra theory, in particular the BGG resolution, can not immediately be used for the Yangian for nonminuscule weights. The absence of the evaluation map poses interesting new questions and requires the development of new methods. We hope to return to these fundamental questions in a future project.

Publications

• “Lax matrices from antidominantly shifted Yangians and quantum affine algebras” (2020)
  R. Frassek, V. Pestun and A. Tsymbaliuk
  (See online at https://doi.org/10.1016/j.aim.2022.108283)
• “Oscillator realisations associated to the D-type Yangian: Towards the operatorial Q-system of orthogonal spin chains,” Nucl. Phys. B 956 (2020), 115063
  R. Frassek
  (See online at https://doi.org/10.1016/j.nuclphysb.2020.115063)
• “QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains,” JHEP 02 (2021), 193
  G. Ferrando, R. Frassek and V. Kazakov
  (See online at https://doi.org/10.1007/JHEP02(2021)19)
• “Rational Lax matrices from antidominantly shifted extended Yangians: BCD types” (2021)
  R. Frassek and A. Tsymbaliuk
  (See online at https://doi.org/10.1007/s00220-022-04345-6)