Supersymmetry algebras that include topological charges

E. Witten; D. Olive

doi:10.1016/0370-2693(78)90357-X

Supersymmetry algebras that include topological charges

E. Witten
, D. Olive

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

801 Scopus citations

Abstract

We show that in supersymmetric theories with solitons, the usual supersymmetry algebra is not valid; the algebra is modified to include the topological quantum numbers as central charges. Using the corrected algebra, we are able to show that in certain four dimensional gauge theories, there are no quantum corrections to the classical mass spectrum. These are theories for which Bogomolny has derived a classical bound; the argument involves showing that Bogomolny's bound is valid quantum mechanically and that it is saturated.

Original language	English (US)
Pages (from-to)	97-101
Number of pages	5
Journal	Physics Letters B
Volume	78
Issue number	1
DOIs	https://doi.org/10.1016/0370-2693(78)90357-X
State	Published - Sep 11 1978
Externally published	Yes

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

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10.1016/0370-2693(78)90357-X

Cite this

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title = "Supersymmetry algebras that include topological charges",

abstract = "We show that in supersymmetric theories with solitons, the usual supersymmetry algebra is not valid; the algebra is modified to include the topological quantum numbers as central charges. Using the corrected algebra, we are able to show that in certain four dimensional gauge theories, there are no quantum corrections to the classical mass spectrum. These are theories for which Bogomolny has derived a classical bound; the argument involves showing that Bogomolny's bound is valid quantum mechanically and that it is saturated.",

author = "E. Witten and D. Olive",

note = "Funding Information: One striking consequence is that, in certain four dimensional theories, we can determine the exact quantum mechanical mass spectrum. In these theories, it turns out that the classical approximation to the mass spectrum (the tree approximation for {"}elementary particles{"}; the semiclassical approximation for solitons) is exact; there are no quantum corrections. For example, in a certain supersymmetric form of the Georgi-Glashow model, with 0(3) broken down to U(1) by the Higgs phenomenon, we can determine the exact mass spectrum: the mass of any particle is the vacuum expectation value of the Higgs field times x/\textasciitilde{} + g2, e and g being the electric and magnetic charges of that particle. 1 Research supported in part by the National Science Founda-tion under Grant No. PHY77-22864.",

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doi = "10.1016/0370-2693(78)90357-X",

language = "English (US)",

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journal = "Physics Letters B",

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T1 - Supersymmetry algebras that include topological charges

AU - Witten, E.

AU - Olive, D.

N1 - Funding Information: One striking consequence is that, in certain four dimensional theories, we can determine the exact quantum mechanical mass spectrum. In these theories, it turns out that the classical approximation to the mass spectrum (the tree approximation for "elementary particles"; the semiclassical approximation for solitons) is exact; there are no quantum corrections. For example, in a certain supersymmetric form of the Georgi-Glashow model, with 0(3) broken down to U(1) by the Higgs phenomenon, we can determine the exact mass spectrum: the mass of any particle is the vacuum expectation value of the Higgs field times x/~ + g2, e and g being the electric and magnetic charges of that particle. 1 Research supported in part by the National Science Founda-tion under Grant No. PHY77-22864.

PY - 1978/9/11

Y1 - 1978/9/11

N2 - We show that in supersymmetric theories with solitons, the usual supersymmetry algebra is not valid; the algebra is modified to include the topological quantum numbers as central charges. Using the corrected algebra, we are able to show that in certain four dimensional gauge theories, there are no quantum corrections to the classical mass spectrum. These are theories for which Bogomolny has derived a classical bound; the argument involves showing that Bogomolny's bound is valid quantum mechanically and that it is saturated.

AB - We show that in supersymmetric theories with solitons, the usual supersymmetry algebra is not valid; the algebra is modified to include the topological quantum numbers as central charges. Using the corrected algebra, we are able to show that in certain four dimensional gauge theories, there are no quantum corrections to the classical mass spectrum. These are theories for which Bogomolny has derived a classical bound; the argument involves showing that Bogomolny's bound is valid quantum mechanically and that it is saturated.

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DO - 10.1016/0370-2693(78)90357-X

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VL - 78

SP - 97

EP - 101

JO - Physics Letters B

JF - Physics Letters B

IS - 1

ER -

Supersymmetry algebras that include topological charges

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