Anomalies of minimal N=(0,1) and N=(0,2) sigma models on homogeneous spaces

Jin Chen, Xiaoyi Cui, Mikhail Shifman, Arkady Vainshtein

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We study chiral anomalies in N= (0, 1) and (0, 2) two-dimensional minimalsigma models defined on the generic homogeneous spaces G/H. Such minimaltheories contain only (left) chiral fermions and in certain cases are inconsistentbecause of incurable? anomalies. We explicitly calculate the anomalous fermioniceffective action and show how to remedy it by adding a series of localcounterterms. In this procedure, we derive a local anomaly matching condition,which is demonstrated to be equivalent to the well-known global topologicalconstraint onp1 (G H), the first Pontryagin class. More importantly,we show that these local counterterms further modify and constrain curable chiral models, some of which, for example, flow to the nontrivial infraredsuperconformal fixed point. Finally, we also observe an interesting relationbetween N = (0, 1) and (0, 2) two-dimensional minimal sigma models andsupersymmetric gauge theories.

Original languageEnglish (US)
Article number025401
JournalJournal of Physics A: Mathematical and Theoretical
Issue number2
StatePublished - Jan 13 2017

Bibliographical note

Funding Information:
X C thanks the Max-Planck Institute for Mathematics in Bonn for their hospitality. The work of M S is supported in part by DOE grant DE-SC0011842. X C is supported by the Dorothea Schlozer Fellowship at the Georg-August Universitat Gottingen.


  • anomalies
  • chiral fermions
  • gauge formulation
  • holonomy
  • homogeneous spaces
  • isometry
  • nonlinear sigma models


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