Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

Abstract

We construct the supercurrent and a supersymmetric current which satisfies the Adler-Bardeen theorem in supersymmetric Yang-Miils theory coupled to non-self-interacting chiral matter. Using the formulatiori recently developed by Grisaru, Milewski, and Zanon, supersymmetry and gauge invariance are maintained with supersymmetric background-field theory and regularization by dimensional reduction. We verify the finiteness of the supercurrent to one loop, and the Adler-Bardeen theorem to two loops by explicit calculations in the minimal-subtraction scheme. We then demonstrate the subtraction-scheme independence of the one-loop Adler-Bardeen anomaly and prove the existence of a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory. Soon after, ones' "solved" the consistency problem in an apparently simple way which also provided an allorders derivation of the / 3 function. His arguments were the following. The component G of the anomaly superfield which contains the axial anomaly has the form If the AB theorem is assumed, the anomalous divergence of the axial-vector current is equal to its one-loop value:Since it is the first component of the supercurrent, the anomalous divergence of j: should also be related to the /3 function and the anomaly superfield component G by Given these assumptions, not only are Eq. (1.2), which represents the AB theorem, and Eq. (1.31, the supercurrent equation, consistent, but they can also be solved for the all-orders /3 function. Amazingly, this procedure gives the correct two-loop value for the /3 function in pure supersymmetric Yang-Mills theory. Jones and

The LHC Higgs Boson Discovery: Updated Implications for Finite Unified Theories and the SUSY Breaking Scale

“…Indeed, it has been shown that the same non-renormalization theorem holds also in SUSY theories [26,70,71]. Therefore: r =hβ (1) g .…”

“…It is based on (a) the structure of the supercurrent in N = 1 SUSY gauge theory [67][68][69] and on (b) the non-renormalization properties of N = 1 chiral anomalies [26,27,66,70,71]. Details on the proof can be found in [27,66] and further discussion in [26,28,[70][71][72].…”

“…Since the gauge symmetry is spontaneously broken below M GUT , the finiteness conditions do not restrict the renormalization properties at low energies, and all that remains are boundary conditions on the gauge and Yukawa couplings (71), the h = −MC (41) relation and the soft scalar-mass sum rule at M GUT .…”

The LHC Higgs boson discovery: Implications for Finite Unified Theories

“…Let us now turn to the all-order finiteness theorem [35,36], which states that if an N = 1 supersymmetric gauge theory can become finite to all orders in the sense of vanishing β-functions, that is of physical scale invariance. It is based on (a) the structure of the supercurrent in N = 1 supersymmetric gauge theory [83][84][85], and on (b) the non-renormalization properties of N = 1 chiral anomalies [35,36,[86][87][88]. Details on the proof can be found in refs.…”

The Higgs boson discovery: recent implications for the Finite Unified Theories and SUSY breaking scale

“…Let us now turn to the all-order finiteness theorem [26,65], which states the conditions under which an N = 1 SUSY gauge theory can become finite to all orders in the sense of vanishing β -functions, that is of physical scale invariance. It is based on (a) the structure of the supercurrent in N = 1 SUSY gauge theory [66][67][68] and on (b) the non-renormalization properties of N = 1 chiral anomalies [25,26,65,69,70]. Details on the proof can be found in [26,65] and further discussion in Refs.…”