Physical attainability of the modified Chern–Simons gauge condition

Determine whether the nonlinear gauge condition b(Ψ₁⋯Ψ_{D−2}) = 0 is physically attainable as a legitimate gauge choice in the modified Chern–Simons theory with D-index antisymmetric structure constants, in order to establish off-shell color–kinematics duality.

Background

The paper introduces a tower of modified Chern–Simons theories whose interaction vertices are built from totally antisymmetric D-index structure constants. The authors derive a nonlinear condition, b(Ψ₁⋯Ψ_{D−2}) = 0, under which the off-shell kinematic Jacobi identity would hold.

The physical status of this condition is unresolved: if it is not a permissible gauge condition, the authors suggest that it might instead be imposed by adding a Lagrange multiplier to the action. Establishing whether the condition is a valid gauge fixing is therefore necessary for determining whether the proposed modified Chern–Simons theories genuinely possess the claimed off-shell color–kinematics structure.