Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit

We study the $S^3$ partition function of three-dimensional supersymmetric $\mathcal{N}=4$ U($N$) SQCD with massive matter multiplets in the infinite mass limit with the so-called Coulomb branch localization. We show that in the infinite mass limit a specific point of the Coulomb branch is selected and contributes dominantly to the partition function. Therefore, we can argue whether each multiplet included in the theory is effectively massless in this limit, even on $S^3$, and conclude that the partition function becomes that of the effective theory on the specific point of the Coulomb branch in the infinite mass limit. In order to investigate which point of the Coulomb branch is dominant, we use the saddle point approximation in the large $N$ limit because the solution of the saddle point equation can be regarded as a specific point of the Coulomb branch. Then, we calculate the partition functions for small rank $N$ and confirm that their behaviors in the infinite mass limit are consistent with the conjecture from the results in the large $N$ limit. Our result suggests that the partition function in the infinite mass limit corresponds to that of an interacting superconformal field theory.Comment: 41 pages, 5 figures; v3: published version in JHE

A Fundamental Limit of Measurement Imposed by the Elementary Interactions

Quantum information theory is closely related to quantum measurement theory because one must perform measurement to obtain information on a quantum system. Among many possible limits of quantum measurement, the simplest ones were derived directly from the uncertainty principles. However, such simple limits are not the only limits. I here suggest a new limit which comes from the forms and the strengths of the elementary interactions. Namely, there are only four types of elementary interactions in nature; their forms are determined by the gauge invariance (and symmetry breaking), and their coupling constants (in the low-energy regime) have definite values. I point out that this leads to a new fundamental limit of quantum measurements. Furthermore, this fundamental limit imposes the fundamental limits of getting information on, preparing, and controlling quantum systems.Comment: 10 pages including 1 figure. Proc. 3rd Tohwa Univ. Int. Conf. Statistical Physics (Fukuoka, Japan, 1999) to be published from AI