Theta-terms in nonlinear sigma-models

A. G. Abanov; P. B. Wiegmann

doi:10.1016/S0550-3213(99)00820-2

Theta-terms in nonlinear sigma-models

A. G. Abanov
, P. B. Wiegmann

Physics and Astronomy

The University of Chicago

Research output: Contribution to journal › Article › peer-review

160 Scopus citations

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.

Original language	English
Pages (from-to)	685-698
Number of pages	14
Journal	Nuclear Physics, Section B
Volume	570
Issue number	3
DOIs	https://doi.org/10.1016/S0550-3213(99)00820-2
State	Published - Mar 27 2000

Keywords

Effective action
Hopf term
Induced charge, spin and statistics of solitons
Sigma-model
Topological terms

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10.1016/S0550-3213(99)00820-2

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AU - Abanov, A. G.

AU - Wiegmann, P. B.

PY - 2000/3/27

Y1 - 2000/3/27

N2 - 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.

AB - 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.

KW - Effective action

KW - Hopf term

KW - Induced charge, spin and statistics of solitons

KW - Sigma-model

KW - Topological terms

UR - https://www.scopus.com/pages/publications/0034719551

U2 - 10.1016/S0550-3213(99)00820-2

DO - 10.1016/S0550-3213(99)00820-2

M3 - Article

AN - SCOPUS:0034719551

SN - 0550-3213

VL - 570

SP - 685

EP - 698

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -

Theta-terms in nonlinear sigma-models

Abstract

Keywords

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