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Holography of Wilson-loop expectation values with local operator insertions

Holography of Wilson-loop expectation values with local operator insertions. Akitsugu Miwa ( Univ. of Tokyo, Komaba ) work in collaboration with Tamiaki Yoneya based on hep-th/0609007. 4-dim, 4, SU(N), SYM. IIB superstring on. AdS 5. boundary.

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Holography of Wilson-loop expectation values with local operator insertions

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  1. Holography of Wilson-loop expectation valueswith local operator insertions Akitsugu Miwa ( Univ. of Tokyo, Komaba ) work in collaboration with Tamiaki Yoneya based on hep-th/0609007

  2. 4-dim, 4, SU(N), SYM IIB superstring on AdS5 boundary present status and aim of this talk: generic loop: difficult circle, straight line: well studied status this talk small deformation of circle or straight line introduction and motivation AdS/CFT correspondence: J.M.Maldacena(1997) Wilson loop in AdS/CFT: S.J.Rey, J.Yee(1998), J.M. Maldacena(1998) Wilson loop string world sheet

  3. deformation of loop and local operator insertion: Wilson loop: deformation of loop: large R-charge local operator insertions: N. Drukker S. Kawamoto (2006)

  4. U(1) sub-group: rotation of a phase of 4 6 5 we consider: string world sheet with large angular momentum SO(6) symmetry: gauge theory side R symmetry : SO(6): ( rotation of 6 scalars ) string theory side isometry on S5 : SO(6) U(1) sub-group: rotation in 5-6 plain corresponding string world sheet: large R-charge

  5. path of large angular momentum mode: path of large angular momentum mode classical path do not reach the boundary because of a potential barrier potential barrier question: SYM side: ? string side: near boundary separated from boundary

  6. ex: 4 6 5 tunneling geodesic: S.Dobashi, H.Shimada, T.Yoneya (2002) tunneling solution correlation function of large R-charge local operators potential barrier today’s talk: we want VEV of Wilson loop: we will study string world sheet around tunneling geodesic path of localized angular momentum

  7. semi-classical approximation of string theory requires large large ‘t Hooft coupling in SYM some comments stringaction: AdS/CFT correspondence: semi-classical approximation:

  8. plan of the talk • introduction and motivation • world sheet with large angular momentum • evaluation of “area” of world sheets • interpretation of results • conclusion and future work

  9. patch1 patch2 AdS5 part: path of localized angular momentum Hamiltonian constraint, EOM: boundary world sheet with large angular momentum metric: S5 part: solution: path of localized angular momentum

  10. comment on non-tunneling solution: N.Drukker, S.Kawamoto (2006) If we use non-tunneling solution, it is difficult to check following relation: tunneling solution: S.Dobashi, H.Shimada, T.Yoneya (2002) tunneling solution (path of localized R-charge) we want: attached to a loop on the boundary world sheet propagating along the tunneling geodesic

  11. circle with radius full world-sheet solution: tunneling geodesic

  12. full world-sheet solution: corresponding Wilson loop:

  13. “area” of a world sheet N.Drukker, D.Gross, H.Ooguri (1999) divergences: singular behavior of the metric . infinite extension of the world sheet . two cutoff schemes world-sheet cutoff: target-space cutoff: w.s. cutoff can be rewritten as: evaluation of “area” of world sheets

  14. results: (const. depends on regularization schemes) consistent with ladder graph calculation

  15. not ladder circle: straight line: in our case consistent with our result interpretation of results ladder graph(planar graph without internal vertex): These results are known to be consistent with the calculation of the area of world sheet without angular momentum. D.Berenstein, R.Corrado, W. Fischler, J.M.Maldacena (1998), N.Drukker, D.J.Gross, H. Ooguri (1999), J.K.Erickson, G.W.Semenoff, K.Zarembo (2000), etc.

  16. and independent finite terms depend on cutoff schemes conclusion and future work conclusion: We have studied open string solution around the tunneling geodesic, the “area” of the world sheet in two cutoff schemes. Main results are ( consistent with ladder graph calculation ) future work: more complicated local operator insertions (more complicated deformation of string world sheet)

  17. SYM side: Wilson loop string side: string world sheet flat conjecture: S.J.Rey, J.Yee(1998); J.M.Maldacena(1998) Wilson loop in AdS/CFT

  18. localized R-charge about Wilson loop

  19. 4-dim, 4, SU(N), SYM IIB superstring on boundary flat introduction and motivation AdS/CFT correspondence: J.M.Maldacena(1997) N D3-brane system

  20. Wilson loop in AdS/CFT: S.J.Rey, J.Yee(1998), J.M. Maldacena(1998) Wilson loop string world sheet AdS5 boundary present status and the aim of this talk: generic loop: difficult circle, straight line: well studied status this talk small deformation of circle or straight line introduction and motivation

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