Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 2

The $\mathsf{CP}^{n-1}$-model with fermions: a new look

Pages: 295 – 324



Dmitri Bykov (Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia; Max-Planck-Institut für Physik, Munich, Germany; and the Arnold Sommerfeld Center for Theoretical Physics, Munich, Germany)


We elaborate the formulation of the $\mathsf{CP}^{n-1}$ sigma model with fermions as a gauged Gross–Neveu model. This approach allows to identify the super phase space of the model as a supersymplectic quotient. Potential chiral gauge anomalies are shown to receive contributions from bosons and fermions alike and are related to properties of this phase space. Along the way we demonstrate that the worldsheet supersymmetric model is a supersymplectic quotient of a model with target space supersymmetry. Possible generalizations to other quiver supervarieties are briefly discussed.

Published 27 December 2022