Theta-terms in nonlinear sigma-models

Details Theta-terms in nonlinear sigma-models Theta-terms in nonlinear sigma-models

1999-11-04

arxiv.org/abs/hep-th/9911025v2

Nucl.Phys. B570 (2000) 685-698

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, no figures, revtex, typos corrected

Scientific paper

10.1016/S0550-3213(99)00820-2

We trace the origin of theta-terms in non-linear sigma-models as a nonperturbative anomaly of current algebras. The non-linear sigma-models emerge as a low energy limit of fermionic sigma-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic sigma-models in spacetime 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 theta-terms. We emphasize a relation between theta-terms and quantum numbers of solitons.

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