Off-shell no-go theorems for higher dimensional supersymmetries and supergravities

Abstract

By a simple fermion counting argument we show in which space-time dimensions the existence of off-shell supersymmetric Yang-Mills and supergravity theories with an off-shell supersymmetry algebra without “central charges” are allowed. In particular we show that the maximally extended theories require “central charges” or lose explicit Lorentz covariance (as in the light-cone gauge), and that for N ⩾ 3, d = 4 only N = 4 supergravity coupled to six Yang-Mills multiplets can avoid the theorems and the off-shell algebra may not have “central charges”.