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Theta-terms in nonlinear sigma-models |
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| Authors: | A. G. Abanov P. B. Wiegmann |
| Affiliation: | a 12-105, Department of Physics, MIT, 77 Massachusetts Ave., Cambridge, MA 02139, USA b James Franck Institute, Enrico Fermi Institute of the University of Chicago, and Landau Institute for Theoretical Physics, 5640 S. Ellis Avenue, Chicago, IL 60637, USA |
| Abstract: | We trace the origin of θ-terms in nonlinear σ-models as a nonperturbative anomaly of current algebras. The nonlinear σ-models emerge as a low energy limit of fermionic σ-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic σ-models in space-time dimension (d+1) with chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres. The geometric phases in the first two hierarchies are θ-terms. We emphasize a relation between θ-terms and quantum numbers of solitons. |
| Keywords: | Topological terms Hopf term Sigma-model Effective action Induced charge, spin and statistics of solitons |
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