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Tomohisa Takimi (NTU )

String solitons in the M5-brane worldvolume with a Nambu-Poisson structure and Seiberg-Witten map. Tomohisa Takimi (NTU ). Ref ) Kazuyuki Furuuchi, T.T JHEP08(2009)050 [arXiv: 0906.3172 ]. M-theory. M-theory: candidate to unify the 5 superstring theory and 11 SUGRA.

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Tomohisa Takimi (NTU )

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  1. String solitons in the M5-brane worldvolume with aNambu-Poisson structure and Seiberg-Witten map TomohisaTakimi (NTU) Ref ) Kazuyuki Furuuchi, T.T JHEP08(2009)050 [arXiv:0906.3172]

  2. M-theory M-theory: candidate to unify the 5 superstring theory and 11 SUGRA Even the fundamental degree of freedom has not been understood well

  3. Recent progress in the ‘M-theory’ (Bagger-Lambert, Phys. Rev. D 77, 065008 (2008)) (A. Gustavsson, Nucl.Phys.B811:66-76,2009) (Aharony-Bergman-Jafferis and Maldacena,  JHEP 0810:091,2008) BLG model Dealing with Multiple membranes ABJM model Studies of these models the deeper understanding about the M-theory

  4. BLG model. N=8 3-d SUSY ‘gauge’ model described by the Lie 3-algebra Originally Formulation of Multiple M2-branes

  5. Action Multiple M2-branes in (1+10) dimensions.

  6. BLG model. Originally Formulation of Multiple M2-branes But also single M5-brane might be included! Ho-Matsuo JHEP 0806:105,2008.  Ho-Imamura-Matsuo and Shiba JHEP 0808:014,2008

  7. Study of ‘the M5-brane’ (Our main purpose)

  8. If we take the dimensional Lie 3-algebra 1. 2. Represent the 3-algebra by the Nambu-Poisson bracket Expansion around the background (M5-brane BPS configuration) 3. BLG can be a ‘M5-brane world-volume’ theory of M2 M5

  9. Non-commutative geometry in the M5-brane ‘The M5-brane’ possesses some ‘Non-commutativity’ with NC-parameter in the worldvolume coordinate After double dimensional reduction to IIA string theory Coincides with the weak limit ( : : a non-commutative parameter) of the D4-brane world-volume theory with non-commutative geometry (written by the Poisson bracket)

  10. About the Seiberg-Witten Map In D-brane theory, These two description is physically equivalent (Just the regularization is different) D-brane in Non-commutativity D-brane in Constant B-field Seiberg-Witten Map (Decided from the fact the gauge transformation of one side must corresponds to the gauge trans. of the other side)

  11. Seiberg-Witten Map in M5 Also in the ‘M5-brane theory’ in BLG model Seiberg-Witten Map is proposed M5-brane in Non-commutativity M5-brane in Constant C-field ( = 0 of BLG M5) First order of the Seiberg-Witten Map is already proposed in Ho-Imamura-Matsuo and Shiba JHEP 0808:014,2008

  12. Open questions (what we try to study)

  13. Although there are several evidences that the BLG would capture the M5-brane information, We are not still sure that ‘the M5-brane in the BLG’ is exactly M5-brane in the M-theory ! We should clarify the relationship between already established M5-brane formulations !

  14. Relationship between the PST formalism Pasti-Sorokin-Tonin Phys. Lett. B 398, 41 (1997) Seiberg-Witten map ? Some limit ? ? PST Formalism (with constant C-field) M5 in BLG model We will study the relationship

  15. How we study the relationship? Comparing M2-brane soliton solution on M5-brane in the both formalism M2 M2 M5 M5 PST Formalism (with constant C-field) BLG Model

  16. Our Works (the study of the M2-brane soliton solution on the M5-brane )

  17. Solution in BLG

  18. Field content and parameter of M5 in BLG :M5-brane world-volume coordinate Direction related with Nambu-poisson bracket :two-form tensor fields :bosonic fields transverse to M5-brane :fermion :SUSY parameter 1-direction 2,3,4,5 direction M5

  19. Anzats for the BPS configuration of M2 on M5 Among the transverse fields is turn on only the 6-direction M2 1-direction 2,3,4,5 direction M5

  20. BPS equation SUSY transformation law of fermion gives BPS equation = 0

  21. BPS equation (Chirality condition of the solution) 1. From the direction M5-brane extends 2. From the direction M2-brane extends

  22. Final form of the BPS equation describing an M2-brane on M5-brane where We solved the equation by the perturbation of

  23. BPS solutionup to O(g) Let us compare this solution with the solution in the PST M5-brane in the constant C-field background

  24. Solution in PST

  25. Relation ship between the solution in the constant C-field in PST formalism Youm , Phys Rev D63 (2001) 045004, Michishita, JHEP 09 (2000) 036 Solution in the constant C-field (residing in 3,4,5-direction ) M2-brane is tilted by for the 2-direction due to the effect of C-field along 3,4,5-direction We take ( << 1) M2 M5

  26. 1. We rotate the coordinate and solution by Rotate the coordinate M2 M2 M5 M5

  27. 2. Performing Seiberg-Witten Map Then we obtained If we take The solution coincides with solution in M5 in BLG!

  28. Indication PST Formalism with C-field M5 in BLG model Connected by Seiberg-Witten Map! These two formalism deeply relate with each other ! The ‘M5-brane’ in BLG would be really M5-brane in M-theory! By some limit, they might translate to each other

  29. Summary We clarified that at least order O(g), M2-soliton on the M5-brane in the Nambu-Poisson bracket can be derived from M2-brane soliton on M5-brane in constant C-field in PST formalism by Seiberg-Witten Map

  30. Future work *All order correspondence between the two actions ? by the Seiberg-Witten Map Need to *study the quantization of Nambu-Poisson bracket, (Our work might also give some hint for this direction. Our direction might be complementary to this study.)

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