Abstract
We continue our investigation on the Nambu-Poisson description of M5-brane in a large constant C-field background (NP M5-brane theory) constructed in refs. [1, 2]. In this paper, the low energy limit where the NP M5-brane theory is applicable is clarified. The background independence of the NP M5-brane theory is made manifest using the variables in the BLG model of multiple M2-branes. An all order solution to the Seiberg-Witten map is also constructed.
Similar content being viewed by others
References
P.-M. Ho and Y. Matsuo, M5 from M2, JHEP 06 (2008) 105 [arXiv:0804.3629] [SPIRES].
P.-M. Ho, Y. Imamura, Y. Matsuo and S. Shiba, M5-brane in three-form flux and multiple M2-branes, JHEP 08 (2008) 014 [arXiv:0805.2898] [SPIRES].
R. Güven, Black p-brane solutions of D = 11 supergravity theory, Phys. Lett. B 276 (1992) 49 [SPIRES].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [SPIRES].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [SPIRES].
P.S. Howe and E. Sezgin, D = 11, p = 5, Phys. Lett. B 394 (1997) 62 [hep-th/9611008] [SPIRES].
P.S. Howe, E. Sezgin and P.C. West, Covariant field equations of the M-theory five-brane, Phys. Lett. B 399 (1997) 49 [hep-th/9702008] [SPIRES].
P. Pasti, D.P. Sorokin and M. Tonin, Covariant action for a D = 11 five-brane with the chiral field, Phys. Lett. B 398 (1997) 41 [hep-th/9701037] [SPIRES].
I.A. Bandos et al., Covariant action for the super-five-brane of M-theory, Phys. Rev. Lett. 78 (1997) 4332 [hep-th/9701149] [SPIRES].
M. Aganagic, J. Park, C. Popescu and J.H. Schwarz, World-volume action of the M-theory five-brane, Nucl. Phys. B 496 (1997) 191 [hep-th/9701166] [SPIRES].
I.A. Bandos et al., On the equivalence of different formulations of the M-theory five-brane, Phys. Lett. B 408 (1997) 135 [hep-th/9703127] [SPIRES].
E. Witten, Five-brane effective action in M-theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234] [SPIRES].
D. Belov and G.W. Moore, Holographic action for the self-dual field, hep-th/0605038 [SPIRES].
J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [SPIRES].
J. Bagger and N. Lambert, Gauge Symmetry and Supersymmetry of Multiple M2-Branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].
A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [SPIRES].
M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048] [SPIRES].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [SPIRES].
K. Furuuchi, S.-Y.D. Shih and T. Takimi, M-Theory Superalgebra From Multiple Membranes, JHEP 08 (2008) 072 [arXiv:0806.4044] [SPIRES].
K. Furuuchi and T. Takimi, String solitons in the M5-brane worldvolume action with Nambu-Poisson structure and Seiberg-Witten map, JHEP 08 (2009) 050 [arXiv:0906.3172] [SPIRES].
P.S. Howe, N.D. Lambert and P.C. West, The self-dual string soliton, Nucl. Phys. B 515 (1998) 203 [hep-th/9709014] [SPIRES].
Y. Michishita, The M2-brane soliton on the M5-brane with constant 3-form, JHEP 09 (2000) 036 [hep-th/0008247] [SPIRES].
D. Youm, BPS solitons in M5-brane worldvolume theory with constant three-form field, Phys. Rev. D 63 (2001) 045004 [hep-th/0009082] [SPIRES].
K. Furuuchi, Non-Linearly Extended Self-Dual Relations From The Nambu-Bracket Description Of M5-Brane In A Constant C-Field Background, JHEP 03 (2010) 127 [arXiv:1001.2300] [SPIRES].
P.S. Howe, E. Sezgin and P.C. West, The six-dimensional self-dual tensor, Phys. Lett. B 400 (1997) 255 [hep-th/9702111] [SPIRES].
J.H. Schwarz, Coupling a self-dual tensor to gravity in six dimensions, Phys. Lett. B 395 (1997) 191 [hep-th/9701008] [SPIRES].
P. Pasti, I. Samsonov, D. Sorokin and M. Tonin, BLG-motivated Lagrangian formulation for the chiral two-form gauge fieldin D =6 and M5-branes, Phys. Rev. D 80 (2009) 086008 [arXiv:0907.4596] [SPIRES].
V.T. Filippov, n-Lie algebras, Sib. Mat. Zh. 26 (1985) 126140.
S. Kawamoto and N. Sasakura, Open membranes in a constant C-field background and noncommutative boundary strings, JHEP 07 (2000) 014 [hep-th/0005123] [SPIRES].
P.-M. Ho and Y. Matsuo, A toy model of open membrane field theory in constant 3-form flux, Gen. Rel. Grav. 39 (2007) 913 [hep-th/0701130] [SPIRES].
C. Hofman and J.-S. Park, Topological open membranes, hep-th/0209148 [SPIRES].
C. Hofman and J.-S. Park, BV quantization of topological open membranes, Commun. Math. Phys. 249 (2004) 249 [hep-th/0209214] [SPIRES].
D.S. Berman and B. Pioline, Open membranes, ribbons and deformed Schild strings, Phys. Rev. D 70 (2004) 045007 [hep-th/0404049] [SPIRES].
C.-S. Chu and D.J. Smith, Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes, JHEP 04 (2009) 097 [arXiv:0901.1847] [SPIRES].
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge Univ. Press, Cambridge U.K. (1998).
C.-S. Chu and P.-M. Ho, Noncommutative open string and D-brane, Nucl. Phys. B 550 (1999) 151 [hep-th/9812219] [SPIRES].
C.-S. Chu and P.-M. Ho, Constrained quantization of open string in background B field and noncommutative D-brane, Nucl. Phys. B 568 (2000) 447 [hep-th/9906192] [SPIRES].
V. Schomerus, D-branes and deformation quantization, JHEP 06 (1999) 030 [hep-th/9903205] [SPIRES].
N. Nekrasov and A.S. Schwarz, Instantons on noncommutative R 4 and (2,0) superconformal six dimensional theory, Commun. Math. Phys. 198 (1998) 689 [hep-th/9802068] [SPIRES].
K. Furuuchi, Instantons on noncommutative R 4 and projection operators, Prog. Theor. Phys. 103 (2000) 1043 [hep-th/9912047] [SPIRES].
K. Furuuchi, Equivalence of projections as gauge equivalence on noncommutative space, Commun. Math. Phys. 217 (2001) 579 [hep-th/0005199] [SPIRES].
P.-M. Ho, Twisted bundle on noncommutative space and U(1) instanton, hep-th/0003012 [SPIRES].
R. Gopakumar, S. Minwalla and A. Strominger, Noncommutative solitons, JHEP 05 (2000) 020 [hep-th/0003160] [SPIRES].
S. Minwalla, M. Van Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics, JHEP 02 (2000) 020 [hep-th/9912072] [SPIRES].
C.-H. Chen, P.-M. Ho and T. Takimi, A No-Go Theorem for M5-brane Theory, JHEP 03 (2010) 104 [arXiv:1001.3244] [SPIRES].
R. Gopakumar, S. Minwalla, N. Seiberg and A. Strominger, OM Theory in Diverse Dimensions, JHEP 08 (2000) 008 [hep-th/0006062] [SPIRES].
N. Seiberg, A note on background independence in noncommutative gauge theories, matrix model and tachyon condensation, JHEP 09 (2000) 003 [hep-th/0008013] [SPIRES].
E. Bergshoeff, D.S. Berman, J.P. van der Schaar and P. Sundell, A noncommutative M-theory five-brane, Nucl. Phys. B 590 (2000) 173 [hep-th/0005026] [SPIRES].
E. Bergshoeff, D.S. Berman, J.P. van der Schaar and P. Sundell, Critical fields on the M5-brane and noncommutative open strings, Phys. Lett. B 492 (2000) 193 [hep-th/0006112] [SPIRES].
G.W. Gibbons and P.C. West, The metric and strong coupling limit of the M5-brane, J. Math. Phys. 42 (2001) 3188 [hep-th/0011149] [SPIRES].
J.P. Van der Schaar, The reduced open membrane metric, JHEP 08 (2001) 048 [hep-th/0106046] [SPIRES].
D.S. Berman et al., Deformation independent open brane metrics and generalized theta parameters, JHEP 02 (2002) 012 [hep-th/0109107] [SPIRES].
E. Bergshoeff and J.P. Van der Schaar, Reduction of open membrane moduli, JHEP 02 (2002) 019 [hep-th/0111061] [SPIRES].
H. Aoki et al., Noncommutative Yang-Mills in IIB matrix model, Nucl. Phys. B 565 (2000) 176 [hep-th/9908141] [SPIRES].
P.-M. Ho, Y. Matsuo and S. Shiba, Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory, JHEP 03 (2009) 045 [arXiv:0901.2003] [SPIRES].
B. Sakita, W (infinity) gauge transformations and the electromagnetic interactions of electrons in the lowest Landau level, Phys. Lett. B 315 (1993) 124 [hep-th/9307087] [SPIRES].
N. Ishibashi, A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176 [SPIRES].
L. Cornalba and R. Schiappa, Matrix theory star products from the Born-Infeld action, Adv. Theor. Math. Phys. 4 (2000) 249 [hep-th/9907211] [SPIRES].
L. Cornalba, D-brane physics and noncommutative Yang-Mills theory, Adv. Theor. Math. Phys. 4 (2000) 271 [hep-th/9909081] [SPIRES].
K. Okuyama, A path integral representation of the map between commutative and noncommutative gauge fields, JHEP 03 (2000) 016 [hep-th/9910138] [SPIRES].
B. Jurčo and P. Schupp, Noncommutative Yang-Mills from equivalence of star products, Eur. Phys. J. C 14 (2000) 367 [hep-th/0001032] [SPIRES].
B. Jurčo, P. Schupp and J. Wess, Noncommutative gauge theory for Poisson manifolds, Nucl. Phys. B 584 (2000) 784 [hep-th/0005005] [SPIRES].
L. Takhtajan, On Foundations of the Generalized Nambu Mechanics, Comm. Math. Phys. 160 (1994) 295 [hep-th/9301111] [SPIRES].
I. Vaisman, A Survey on Nambu-Poisson Brackets, math/9901047.
T. Asakawa and I. Kishimoto, Comments on gauge equivalence in noncommutative geometry, JHEP 11 (1999) 024 [hep-th/9909139] [SPIRES].
Y. Okawa and S. Terashima, Constraints on effective Lagrangian of D-branes from non-commutative gauge theory, Nucl. Phys. B 584 (2000) 329 [hep-th/0002194] [SPIRES].
W.-M. Chen and P.-M. Ho, Lagrangian Formulations of Self-dual Gauge Theories in Diverse Dimensions, Nucl. Phys. B 837 (2010) 1 [arXiv:1001.3608] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1006.5291
Rights and permissions
About this article
Cite this article
Chen, CH., Furuuchi, K., Ho, PM. et al. More on the Nambu-Poisson M5-brane theory: scaling limit, background independence and an all order solution to the Seiberg-Witten map. J. High Energ. Phys. 2010, 100 (2010). https://doi.org/10.1007/JHEP10(2010)100
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2010)100