AdS/CFT対応を用いたクォーク間力のカオスの解析
太田敏博
大阪大学

Collaboration with T. Akutagawa, K. Hashimoto, K. Murata
arXiv:1901.XXXXXAdS/CFT対応を用いたクォーク間力のカオスの解析

場の量子論のカオスをどう測るか？
Wilsonループの時間発展はどれくらいカオスか？
セットアップ
AdS/CFT対応を用いてD4ソリトン時空中の弦の運動を解析する

太田敏博

太田敏博

AdS/CFT対応を用いたクォーク間力のカオスの解析

Wilsonループとしての開弦[Maldacena, Rey-Yee]

時空の境界q<latexit sha1_base64="Ag6XMyr58orstnV08RCdBEZe1ag=">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</latexit>q̄<latexit sha1_base64="HdWGU6r0YzrUOREqP2Yp6OKAu9g=">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</latexit>

時空の境界から伸びる開弦のon-shell作用＝クォーク間ポテンシャル太田敏博

AdS/CFT対応を用いたクォーク間力のカオスの解析

D4時空上の弦の運動
弦の端点にZ2対称な摂動を加える• 弦の中心に注目し、カオスを見る•

D4-boundaryq<latexit sha1_base64="Ag6XMyr58orstnV08RCdBEZe1ag=">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</latexit>

rcenter<latexit sha1_base64="IE32uRIo/c9pAfXZzinYOlE058c=">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</latexit>q̄<latexit sha1_base64="KiMbOvdY4rpUaA6Zf5ynsB8+ZA8=">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</latexit>

rcenter<latexit sha1_base64="HdWGU6r0YzrUOREqP2Yp6OKAu9g=">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</latexit>t<latexit sha1_base64="IcHcZsjhnwNwjDlQgpROzuao6SU=">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</latexit><latexit太田敏博

AdS/CFT対応を用いたクォーク間力のカオスの解析

結論
D4時空上の弦の運動はカオス的＝対応するゲージ理論でクォーク間に働く力は初期摂動に対して鋭敏である✏|h F~ (t)i|

カオスの相図クォーク間力のカオス<latexit sha1_base64="zfiiWBXbQj1rdgp/M9iVyWzrRfY=">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</latexit><latexit sha1_base64="c7zUFGJ8Svrxk7vb3cS2yzMsO7Y=">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</latexit><latexit

Lq<latexit sha1_base64="hMTmat94J+1f1WOL8FOxrrVsMFk=">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</latexit>t<latexit sha1_base64="+HKFG4gLqZ6eWxEsYw4M5ybxZ78=">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</latexit><latexithF~ (t)i =<latexit sha1_base64="ljMJf/DG/5c6RPeGw856UFjya6U=">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</latexit>

72⇡~ r)|boundary@r4 X(t,