論文

査読有り
2007年6月

Zonotopes and four-dimensional superconformal field theories

JOURNAL OF HIGH ENERGY PHYSICS
  • Akishi Kato

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.

Web of Science ® 被引用回数 : 8

リンク情報
DOI
https://doi.org/10.1088/1126-6708/2007/06/037
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000247900400050&DestApp=WOS_CPL

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