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Machiko HATSUDA 　（ KEK ＆ Urawa Univ. ）

Nonlocal Chrages of T-dual strings. ( JHEP 0607:029, 2006 S. Mizoguchi & M.H.). Machiko HATSUDA 　（ KEK ＆ Urawa Univ. ）. I. Introduction II. Flat space III. pp-wave space III-i. IIB pp-wave space III-ii. Before and after T-duality IV. Conclusions. I. Introduction.

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Machiko HATSUDA 　（ KEK ＆ Urawa Univ. ）

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  1. Nonlocal Chrages of T-dual strings (JHEP 0607:029, 2006 S. Mizoguchi & M.H.) Machiko HATSUDA　（KEK＆Urawa Univ.） I. Introduction II. Flat space III. pp-wave space III-i.IIB pp-wave space III-ii.Before and after T-duality IV. Conclusions

  2. I. Introduction • Integrability is useful to explore new string backgrounds corresponding to gauge theory duals. • Minahan & Zarembo ’02, spin chain models,… • T-duality is also useful to explore new string background. • Lunin & Maldacena ’05, Mirror, T-fold, … ⇒Is there any relation between integrability & T-duality which are both useful to explore string backgrounds? ＠HAWAII　2006, 10/30

  3. Current conservation: Integrable, ex.S-matrix factorization, suppression of particle production Conservation: Flatness: ＠HAWAII　2006, 10/30

  4. Before T-dual (IIB pp-wave) Infinite number of nonlocal charges exists After T-dual (IIA pp-wave) Flatness is broken by “BNS/NS” ! Conventional derivation can not lead to infinite number of nonlocal charges! Results & puzzle Puzzle: Are there infinite number of nonlocal charges after T-dual? ? • Results: • Quantum nonlocal charges are obtained. • Noether charges of T-dual string was included here! ! ＠HAWAII　2006, 10/30

  5. II. Flat space • Action • Noether currents • Flatness • Quantization ＠HAWAII　2006, 10/30

  6. Noether charges • 1-st nonlocal charges • 2-nd & higher nonlocal charges are not independent ＠HAWAII　2006, 10/30

  7. Nonlocal charges in flat space Before T-dual After T-dual T-dual transf. interchanges 0-th & 1-st nonlocalcharges！ ＠HAWAII　2006, 10/30

  8. pp-wave space III-i. IIB pp-wave space • IIB pp-wave action • Quantization RR flux ＠HAWAII　2006, 10/30

  9. 0-th charges: 1-st nonlocal charges: 2-nd nonlocal charges: Alday ‘03 Mizoguchi & M.H. ‘06 Infinite number of nonlocal charges exist in pp-wave space！ ＠HAWAII　2006, 10/30

  10. III-ii. Before and after T-duality Michelson ‘02 • Michelson’s IIB pp-wave action • Compactify direction • T-dualized IIA pp-wave action Non-zero B ! ＠HAWAII　2006, 10/30

  11. Nonlocal charges in pp-wave space Before T-dual ( IIB ) After T-dual( IIA ) Same lightcone Hamiltonian IIA Noether charges are Included in IIB nonlocal charges！ ＠HAWAII　2006, 10/30

  12. Bonus of “nonlocal charge/T-duality relation” • To complete our correspondence: • Noether charge in IIA/1-st nonlocal charge in IIB • Buscher’s T-duality transf. may be Wess-Zumino term in IIB action： • IIA and IIB pp-wave algebras are satisfied consistently : →Conjugate of winding mode is introduced in original IIB side naturally ＠HAWAII　2006, 10/30

  13. IV. Conclusions quantum nonlocal charges • We have obtained in flat &pp-wave spaces. • We have shown that: interchanges odd & even nonlocal charges in flat space. IIA pp-wave space Noether charge is included as the 1-st nonlocal charge in the original IIB pp-wave space. • Conjugate of winding mode is introduced naturally. • We leave a puzzle - computation of nonlocal charges in IIA pp-wave space- for future investigation. T-duality T-dualized T-dualized ＠HAWAII　2006, 10/30

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