Skip to main content Accessibility help
×
Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-07T13:18:56.087Z Has data issue: false hasContentIssue false

20 - The problem of gauging supersymmetry

Published online by Cambridge University Press:  01 June 2011

Get access

Summary

The fundamental symmetries exhibited by the laws of nature are local rather than global, i.e. they are gauged. This is certainly true, say, of SU(3)color and [SU(2) × U(1)]electroweak. If the laws of nature turn out to exhibit some form of supersymmetry, it is then natural to ask whether supersymmetry can also be gauged. As we saw, all (N = 1 and N > 1) supersymmetries in four dimensions contain the Poincaré (or de-Sitter) algebra as a subalgebra. Gauging supersymmetry thus implies gauging the Poincaré or de-Sitter algebras. But such a gauge theory of the Poincaré or de-Sitter algebras is the Einstein theory of gravity (Kibble 1961). When gauging supersymmetry, gravity then must be included. This gives us an idea about the gauge fields to be expected when supersymmetry is gauged. Gravity is described by a massless spin two boson. Then at the very least, for local N = 1 supersymmetry we expect this spin two graviton to acquire a supersymmetric partner. Purely on representation–theoretic grounds (see chapter 5) this partner must be a massless fermion of spin three-halves or five-halves. The supersymmetry charges Qα span a (spin one-half) Majorana spinor. The corresponding gauge field having one vector index beyond that of the charges, will describe spin three-halves, not five-halves. So the N = 1 supergravity multiplet contains one massless spin two boson, the graviton, and one Majorana spin three-halves fermion (Volkov & Akulov 1973) the gravitino.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×