Seminars

ハドロン物理セミナーでは、気鋭の研究者に最近の研究のお話をしていただきます。

We invite spirited researchers as speakers of the Hadron Physics Seminar.

*  以下の時間は、UTC + 9である日本標準時（JST）です。

*  The schedule below is in terms of Japan Standard Time (JST), namely UTC +9.

Mon, June 16th

Dimensional reduction gauge and effective dimensional reduction in four-dimensional Yang-Mills theory 

Kei Tohme (Kyoto Univ.)
Room 907 (16:00-18:00)

Abstract: Motivated by one-dimensional color-electric flux-tube formation in four-dimensional (4D) QCD, we investigate a possibility of effective dimensional reduction in the 4D Yang-Mills (YM) theory. We propose a new gauge fixing of “dimensional reduction (DR) gauge” defined so as to minimize 𝑅_{DR} ≡∫𝑑^4 ⁢𝑠⁢Tr⁡[𝐴^2_𝑥⁡(𝑠)+𝐴^2_𝑦⁡(𝑠)], which has a residual gauge symmetry for the gauge function Ω⁡(𝑡,𝑧) like 2D QCD on the 𝑡−𝑧 plane. We investigate effective dimensional reduction in the DR gauge using SU(3) quenched lattice QCD at 𝛽 =6.0. The amplitude of 𝐴𝑥⁡(𝑠) and 𝐴𝑦⁡(𝑠) are found to be strongly suppressed in the DR gauge. We consider “𝑡⁢𝑧-projection” of 𝐴_{𝑥,𝑦}⁡(𝑠) →0 for the gauge configuration generated in the DR gauge, in a similar sense to Abelian projection in the maximally Abelian gauge. By the 𝑡⁢𝑧-projection in the DR gauge, the interquark potential is not changed, and 𝐴𝑡⁡(𝑠) and 𝐴𝑧⁡(𝑠) play a dominant role in quark confinement. In the DR gauge, we calculate a spatial correlation ⟨Tr⁡𝐴_⊥⁡(𝑠)⁢ 𝐴_⊥⁡(𝑠 +𝑟⁢𝑎_⊥)⟩⁢(⊥ =𝑥,𝑦) and estimate the spatial mass of 𝐴_⊥⁡(𝑠)⁢(⊥ =𝑥,𝑦) as 𝑀 ≃1.7 GeV. It is conjectured that this large mass makes 𝐴_⊥⁡(𝑠) inactive and realizes the dominance of 𝐴_𝑡⁡(𝑠) and 𝐴_𝑧⁡(𝑠) in infrared region in the DR gauge. We also calculate the spatial correlation of two temporal link-variables and find that the correlation decreases as exp⁡(−𝑚⁢𝑟) with 𝑚 ≃0.6 GeV. Using a crude approximation, the 4D YM theory is reduced into an ensemble of 2D YM systems with the coupling of 𝑔_2⁢D =𝑔⁡𝑚.