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 TMF, 1987, Volume 71, Number 2, Pages 193–207 (Mi tmf4931)

Duality in $d=2$ $\sigma$ models of chiral field with anomaly

E. A. Ivanov

Abstract: Using a manifestly geometric language of Cartan forms, we expose continuous dual symmetry of general $d=2$ models of chiral field with anomaly (ACF) (also called the $d=2$ sigma-models with multivalued action) and find the corresponding duality transformations. Both ordinary and supersymmetric ACF are treated. Like in the case of the standard chiral field, duality transformations of ACF prove to be related intimately to its integrability. We introduce also the notions of dual algebra and dual sigma-model and demonstrate their important role for understanding the classical and quantum structure of ACF. It is shown, in particular, that the transition to infrared fixed points of ACF models can be described in a pure algebraic way as a contraction of the dual algebra, as a result of which the coset space of the dual sigma-model becomes flat. Finally, we analyze, in an analogous context, the classical equations of the anomalous version of $CP^1$-model. These are found to yield a trivial dynamics.

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English version:
Theoretical and Mathematical Physics, 1987, 71:2, 474–484

Bibliographic databases:

Citation: E. A. Ivanov, “Duality in $d=2$ $\sigma$ models of chiral field with anomaly”, TMF, 71:2 (1987), 193–207; Theoret. and Math. Phys., 71:2 (1987), 474–484

Citation in format AMSBIB
\Bibitem{Iva87} \by E.~A.~Ivanov \paper Duality in $d=2$ $\sigma$ models of chiral field with anomaly \jour TMF \yr 1987 \vol 71 \issue 2 \pages 193--207 \mathnet{http://mi.mathnet.ru/tmf4931} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=911667} \transl \jour Theoret. and Math. Phys. \yr 1987 \vol 71 \issue 2 \pages 474--484 \crossref{https://doi.org/10.1007/BF01028646} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987L510600003} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. A. Ivanov, A. P. Isaev, “The Green–Schwarz superstring as an asymmetric model of a chiral field”, Theoret. and Math. Phys., 81:3 (1989), 1304–1313
2. Cabrera, A, “Hamiltonian loop group actions and T-duality for group manifolds”, Journal of Geometry and Physics, 56:7 (2006), 1116
3. Sarisaman M., “Euclidean Pseudoduality and Boundary Conditions in SIGMA Models”, Nucl. Phys. B, 868:1 (2013), 314–327
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