Finiteness Properties of the N=4 Super-Yang--Mills Theory in Supersymmetric Gauge

Abstract

With the introduction of shadow fields, we demonstrate the renormalizability of the N=4 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 $\beta$ 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.

arXiv comment27

References in corpus (7)

• Special Quantum Field Theories In Eight And Other Dimensions
• Perturbative Beta Function of N=2 Super Yang-Mills Theories
• Shadow Fields and Local Supersymmetric Gauges
• Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry
• Protected Operators in N=2,4 Supersymmetric Theories
• An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories
• New Results on N=4 SuperYang-Mills Theory

Cited by in corpus (12)

• The ultra-violet question in maximally supersymmetric field theories
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• Ten-dimensional super-Yang-Mills with nine off-shell supersymmetries
• SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry
• Perturbative linearization of super-Yang-Mills theories in general gauges
• On the irrelevance of the Gribov issue in N=4 Super Yang-Mills in the Landau gauge
• Superconformal invariance from N=2 supersymmetry Ward identities
• Supersymmetric renormalization prescription in N = 4 super-Yang--Mills theory
• N=4 Yang--Mills theory as a complexification of the N=2 theory
• Twisted Superalgebras and Cohomologies of the N=2 Superconformal Quantum Mechanics
• Four twisted differential operators for the N=4 superconformal algebra
• Shadows and Twisted Variables