Finiteness properties of the image super-Yang–Mills theory in supersymmetric gauge Original Research Article

With the introduction of shadow fields, we demonstrate the renormalizability of the image super-Yang–Mills theory in component formalism, independently of the choice of UV regularization. Remarkably, by using twisted representations, one finds that the structure of the theory and its renormalization is determined by a subalgebra of supersymmetry that closes off-shell. Starting from this subalgebra of symmetry, we prove some features of the superconformal invariance of the theory. We give a new algebraic proof of the cancellation of the β function and we show the ultraviolet finiteness of the 1/2 BPS operators at all orders in perturbation theory. In fact, using the shadow field as a Maurer–Cartan form, the invariant polynomials in the scalar fields in traceless symmetric representations of the internal R-symmetry group are simply related to characteristic classes. Their UV finiteness is a consequence of the Chern–Simons formula.