Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-07-14
JHEP 0006:030,2000
Physics
High Energy Physics
High Energy Physics - Theory
35 pages, LaTeX, no special macros
Scientific paper
10.1088/1126-6708/2000/06/030
There have been known "exact" beta functions for the gauge coupling in N=1 supersymmetric gauge theories, the so-called NSVZ beta functions. Shifman and Vainshtein (SV) further related these beta functions to the exact 1-loop running of the "Wilsonian" gauge coupling. All these results, however, remain somewhat mysterious. We attempt to clarify these issues by presenting new perspectives on the NSVZ beta function. Our interpretation of the results is somewhat different than the one given by SV, having nothing to do with the distinction between "Wilsonian" and "1PI" effective actions. Throughout we work in the context of the Wilsonian Renormalization Group; namely, as the cutoff of the theory is changed from M to M', we determine the appropriate changes in the bare couplings needed to keep the low energy physics fixed. The entire analysis is therefore free of infrared subtleties. When the bare Lagrangian given at the cutoff is manifestly holomorphic in the gauge coupling, we show that the required change in the holomorphic gauge coupling is exhausted at 1-loop to all orders of perturbation theory, and even non-perturbatively in some cases. On the other hand, when the bare Lagrangian has canonically normalized kinetic terms, we find that the required change in the gauge coupling is given by the NSVZ beta function. The higher order contributions in the NSVZ beta function are due to anomalous Jacobians under the rescaling of the fields done in passing from holomorphic to canonical normalization. We also give prescriptions for regularizing certain N=1 theories with an ultraviolet cutoff M preserving manifest holomorphy, starting from finite N=4 and N=2 theories. It is then in principle possible to check the validity of the exact beta function by higher order calculations in these theories.
Arkani-Hamed Nima
Murayama Hitoshi
No associations
LandOfFree
Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-154389