| 講師 | Dmitri Diakonov (INP, St. Petersburg/Nordita) |
|---|---|
| タイトル | Gauge invariant dual variables in the 4-dimensional Yang-Mills theory |
| 日時 | 2006年5月10日(水) 11:00-12:30 |
| 場所 | (未定) |
| 連絡先 | 理学部物理学科素粒子論研究室 セミナー係 小野謙仁 |
| 概要 | The partition function of the SU(2) Yang--Mills theory is rewritten in terms of gauge invariant variables related to the dual field strength. The new variables are the 4-dimensional metric of the dual space $g_{\mu\nu}$ and an additional 3-dimensional metric $h_{ij}$ related to the gauge group. The action is a sum of two terms: one is invariant under a large group of local transformations which include general coordinate transformations. It reduces to the Einstein--Hilbert action if the 3-dimensional metric is trivial. The other term is not invariant and hence distinguishes the Yang--Mills theory from quantum gravity. The de Sitter dual space is a saddle point of the Yang--Mills theory in this formulation. Integrating over small oscillations about the de Sitter space reproduces the asymptotic freedom coefficient ``11/3''. Large general coordinate transformations are described by an $O(5)$ sigma model in 4 dimensions. Setting $5=n$ to be a formal algebraic parameter we show that at large $n$ the diffeomorphisms acquire a mass through the dimensional transmutation, thus suggesting a new mechanism of the spontaneous mass generation in the unbroken pure Yang--Mills theory. |
