An Off‐Shell Superspace Reformulation of D = 4, N = 4 Super‐Yang–Mills Theory

A Minimal b Ghost

“…This will certainly apply also to the operators used in the action of $$D=11$$ supergravity [ 4,5 ] and to any other models. [ 24–29 ] There may be a certain advantage in using the minimal operators. The interpretation of the operators typically is that they map between different cohomology classes, and those are most simply represented in the minimal picture.…”

10D super-Yang-Mills scattering amplitudes from its pure spinor action

“…Color-kinematics duality followed directly from the second order nature of the b-ghost, without kinematic structure constants appearing in the action, so it would be interesting to find other theories with a similar action and propagator-numerator. Since it has been observed that the colorkinematics duality has connections to supersymmetry [62], exploring pure spinor type formulations of theories in lower dimensions [5,63,64] seems promising. Perhaps in lower dimensions numerators would be more tractable for direct computations.…”

Pure spinor superspace action for D = 6, N = 1 super-Yang-Mills theory

“…In order for a nonscalar superfield to carry a cohomology which is not a product of its representation and the scalar cohomology, it has to be subject to some condition. This has been encountered in a number of situations [2,3,5,6,8,13], and was named "shift" symmetry in ref. [8].…”

“…Even more drastic reduction of the order of the interactions are seen in the actions for BLG and ABJM models [2][3][4], in the Born-Infeld deformation of D = 10 SYM [8,11,12], and in D = 11 supergravity [5,6]. The equations of motion following from the action (4.12) are 13) where "•" is shorthand for formation of the adjoint of the gauge algebra, and [·, ·] denotes adjoint action. Note that gauge field interactions are introduced by deformation (covariantisation) of the cohomology, while the matter current back-reacts on the SYM fields through a deformation of the condition on the auxiliary fields (the current multiplet).…”

“…[1] and references therein) have been used in the construction of actions for maximally supersymmetric theories [2][3][4][5][6][7][8][9][10][11][12][13]. It is there that the formalism, originating in superstring theory [14][15][16][17] and in the deformation theory for maximally supersymmetric super-Yang-Mills theory (SYM) and supergravity [18][19][20][21][22][23][24][25], has its greatest power.…”