2007年6月
Zonotopes and four-dimensional superconformal field theories
JOURNAL OF HIGH ENERGY PHYSICS
- 巻
- 号
- 6
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1088/1126-6708/2007/06/037
- 出版者・発行元
- SPRINGER
The a-maximization technique proposed by Intriligator and Wecht allows us to determine the exact R-charges and scaling dimensions of the chiral operators of four-dimensional superconformal field theories. The problem of existence and uniqueness of the solution, however, has not been addressed in general setting. In this paper, it is shown that the a-function always has a unique critical point which is also a global maximum for a large class of quiver gauge theories specified by toric diagrams. Our proof is based on the observation that the a-function is given by the volume of a three dimensional polytope called "zonotope", and the uniqueness essentially follows from Brunn-Minkowski inequality for the volume of convex bodies. We also show a universal upper bound for the exact R-charges, and the monotonicity of a-function in the sense that a-function decreases whenever the toric diagram shrinks. The relationship between a-maximization and volume-minimization is also discussed.
- リンク情報
- ID情報
-
- DOI : 10.1088/1126-6708/2007/06/037
- ISSN : 1029-8479
- Web of Science ID : WOS:000247900400050