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Pei-Ming Ho Department of Physics, NTU March 2006

Spacetime for Strings. Spacetime for Strings. Pei-Ming Ho Department of Physics, NTU March 2006. What is spacetime?. Spacetime in Einstein’s theory. The Riemannian geometric property (notion of distance and curvature, etc.) of the spacetime is dynamically determined by the theory.

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Pei-Ming Ho Department of Physics, NTU March 2006

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  1. Spacetime for Strings Spacetime for Strings Pei-Ming Ho Department of Physics, NTU March 2006

  2. What is spacetime?

  3. Spacetime in Einstein’s theory • The Riemannian geometric property (notion of distance and curvature, etc.) of the spacetime is dynamically determined by the theory. • Gravity geometrized. • Field equations determine the motion of particles.

  4. Why is D = 3+1 ?

  5. Einstein’s theory vs. Strings • The dimension of spacetime, the geometric structure (Riemann) are put in by hand. • Singularities. • Quantization?information paradox • String theory is a consistent (and computable) theory of quantum gravity approximated by Einstein’s theory at low energies.

  6. at Planck scale A naïve combination of GR and QM suggests that the classical notion of spacetime breaks down at the Planck scale (1019 GeV, 10-33 cm). m

  7. What is quantum spacetime?We need a theory of quantum gravity.String theory is essentially our only hope.

  8. What is string theory? particle → string

  9. oscillation modes → particles

  10. unique interaction

  11. solitons • There are solitons called D-branes. • D-branes come in various dimensions. • There are open strings ending on D-branes.

  12. This idea about strings leads to very complicated mathematical problems, but surprisingly the theory has many nice and interesting properties.

  13. “弦論” 符合網頁(2001) 1. UFO: • 飛碟到底從哪裡來？ • …克氏理論」有五維的時空，以及「超弦理論」有十維的時空。目前科學家矚目的「超弦理論(superstring theory)」，是根據「超對稱(supersymmetry)」和「弦論(string theory)」兩個理論結合的一種最新的物理理論。 • 外星人與飛碟真相的研究。 • 從幽浮現象探討宇宙三度空間 ∙

  14. 2. News: • 科學家以世界最大的望遠鏡觀察宇宙，發現光速並非常數，… • 霍金預言百年後人類將殖民外星… ∙ 3. Not related to string theory YET: • 撥動陽光之弦－論槐華詩歌的美學追求… • 吳弦，論指揮管制戰的真義… • 『紀弦論現代詩』… • 前者以趺陽脈弦論病，這條是以寸口脈弦論病… ∙

  15. 4.科普介紹： • 光與物質小站… • 科學討論區… • 複雜的時空…超弦理論也存在著困難… • 加賀先生在弦論相關領域的研究上有相當的知名度… • 史蓋皮諾立刻向貝尼特說出他目前的研究計畫，那是叫做「弦論」的玩意，處理次原子世界的現象 ∙

  16. 5.學術界： • 李仁吉教授，美國賓州大學物理博士，專長：場論、弦論。 • http://www.phys.ntu.edu.tw/~pmho 台大弦論小組的網站 ∙

  17. “弦論” 符合網頁(2006)約有34,000項符合弦論的查詢結果 1. 科普介紹： 光與物質小站 科學人 弦論通俗演義 博客李淼 討論區(如：北一女中地球科學討論區) ∙ 2. 學術界… 3. Not related to string theory YET: 二胡專輯《胡弦論雨》 七弦論考 ∙

  18. Strings everywhere!

  19. about string theory • String theory is not yet experimentally verified. (But this is not a geometry-independent question…) • String Theory includes Quantum Gravity. • The spacetime is 10 dimensional for superstring theory (11 for M theory,12 for F theory,5 for IIB in AdS,1 for BFSSand 0 for IKKT).

  20. Kaluza-Klein w. Calabi-Yau

  21. Brane World Brane World

  22. fundamental strings • Spacetime = target space of the fields living on the string worldsheet: • Dimension is determined by symmetry. • High energy limit is smooth, not spiky. • Change of variables / field redefinition  different interpretation of spacetime

  23. T-duality Winding modes are interchanged with momentum modes.

  24. probe-dependence • fundamental string or soliton (D-brane) « S-duality interchanges F1 and D1. » • Geometric properties can not be completely separated from interactions. Example: Noncommutative geometry [ x, y ] = ic  Δx Δy ≥ c

  25. theory-dependence • M theory (11D)  IIA superstring theory (10D) • All 5 superstring theories are equivalent. • Holography: Q. Gravity in higher dimensions  Local field theories in lower dimensions. Example: AdS/CFT duality. IIB superstring in AdS  SYM in 4 dim.

  26. 道可道非常道 名可名非常名

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