Supersymmetric Yang-Mills equations and supertwistors
Abstract
This paper is a survey of results relating the supertwistor correspondence on N-extended super-Minkowski space M4|4 N to supersymmetric Yang-Mills (SSYM) theory. A theorem of Manin relating bundles on the (3- N)th infinitesimal neighborhood L(3- N) 5|2 N of super null-line space L 5/2N → P3/N× P3/N∗ to solutions of the SSYM equations is analyzed in terms of component fields, interpolating between the N = 0 and N = 3 results studied previously. Using an inductive approach based on the degree of odd homogeneity and a particular gauge condition (the D-gauge), the graded Frobenius equations for covariant constancy along super null-lines are solved. The resulting solution space is shown to define a bundle over L5|2 N which extends to L(3- N) 5|2 N when the SSYM equations are satisfied. Conversely, the inverse transform determines super connections that are integrable along super null-lines in M4|4 N. These superconnections determine a supermultiplet which solves the SSYM equations when the bundle over L5|2 N extends to L(3- N) 5|2 N. A clarification is given concerning the relation between supersymmetry transformations of the component fields and Lie derivations of superconnections on M4|4 N satisfying super null-line integrability conditions and the D-gauge conditions. Our approach is aimed at bridging the gap between the abstract sheaf-theoretic formulation preferred by mathematicians and the coordinate formulation familiar to physicists.
- Publication:
-
Annals of Physics
- Pub Date:
- July 1989
- DOI:
- 10.1016/0003-4916(89)90351-5
- Bibcode:
- 1989AnPhy.193...40H