Abstract
We show that the Hamiltonian of (N=1;d=10) super Yang-Mills can be expressed as a quadratic form in a very similar manner to that of the (N=4;d=4) theory. We find a similar quadratic form structure for pure Yang-Mills theory but this feature, in the non-supersymmetric case, seems to be unique to four dimensions. We discuss some consequences of this feature.
Highlights
Maximally supersymmetric theories, among the supersymmetric ones, that exhibit this property
We find a similar quadratic form structure for pure Yang-Mills theory but this feature, in the non-supersymmetric case, seems to be unique to four dimensions
If we could successfully ‘lift’ or ‘oxidize’ this quadratic form structure to eleven dimensions, the eleven-dimensional theory would exhibit E7(7) invariance assuming that the ‘lifting’ process commutes with the exceptional generators
Summary
This section serves as a brief review of the results in [1, 8] relevant to this paper. With the introduction of anticommuting Grassmann variables θm and θm (m, n, p, q, · · · = 1, 2, 3, 4, denote SU(4) spinor indices), all the physical degrees of freedom can be captured in one superfield φ (y). The supersymmetry generators are of two varieties: kinematical and dynamical. The kinematical (spectrum generating) supersymmetries q m +. While the dynamical supersymmetries are obtained by boosting the kinematical ones qm−. For the dynamical (non-linear) generators, we have to find non-linear terms such that the algebra closes. The key ingredient in proving this is the use of the “inside-out constraint” (2.8) This point is important since it implies that other supersymmetric Yang-Mills theories cannot be expressed as simple quadratic forms since those theories have no such constraint on the superfield
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
