nLab Nambu-Poisson M5-brane model

Idea

The Nambu-Poisson M5-brane model (NP-M5 model, due to Ho & Matsuo 2008, so named by Chen, Furuuchi, Ho & Takimi 2010) is a sigma-model for a 5-branes on worldvolumes of product form $\Sigma^{1,5} \simeq \Sigma^{1,2} \times X^{3}$ carrying large and constant 3-form flux density, which is meant to coincide with the standard M5-brane sigma-model in this situation (though there may remain gaps in making this precise, cf. KSV 2013).

The NP M5-model is in fact the BLG model for M2-branes on $\Sigma^{1,2}$ , but with the latter’s controlling M-brane 3-algebra taken to locally be the Nambu-Poisson bracket on the smooth functions over $\mathbb{R}^3$ , globalized to $X^3$ by a gauge symmetry of volume-preserving diffeomorphisms. Since the vector space of smooth functions on $X^3$ is not finite-dimensional, one interprets this construction as a kind of condensation of infinitely many coincident M2-branes which “polarize” into an M5-brane in an M-theoretic version of the Myers effect (by which, ordinarily, $D_{p-2}$ -branes polarize to a $D_p$ -brane in a constant RR-field flux density backgrounds).

On the Nambu-Poisson M5-brane model — a sigma-model for M5-branes with product worldvolume $\Sigma^{1,5} \simeq X^{1,2} \times Y^3$ carrying large constant $H_3$ flux density — obtained via an M-theoretic version the of Myers effect from the BLG model for coincident M2-branes with worldvolume $X^{1,2}$ , by taking the latter’s controlling M-brane 3-algebra to be the Nambu bracket on the smooth functions over the 3-manifold $Y^3$ (globalized via VPD gauge symmetry).

The original articles:

Pei-Ming Ho, Yutaka Matsuo: M5 from M2, JHEP06 (2008) 105 [doi:10.1088/1126-6708/2008/06/105, arXiv:0804.3629]
Pei-Ming Ho, Yosuke Imamura, Yutaka Matsuo, Shotaro Shiba: M5-brane in three-form flux and multiple M2-branes, JHEP 0808:014 (2008) [doi:10.1088/1126-6708/2008/08/014, arXiv:0805.2898]
Paolo Pasti, Igor Samsonov, Dmitri Sorokin, Mario Tonin: BLG-motivated Lagrangian formulation for the chiral two-form gauge field in $D=6$ and M5-branes, Phys. Rev. D 80 (2009) 086008 [doi:10.1103/PhysRevD.80.086008, arXiv:0907.4596]
Andreas Gustavsson: M5 brane from mass deformed BLG theory, JHEP 11 (2009) 071 [doi:10.1088/1126-6708/2009/11/071, arXiv:0909.2518]
Kazuyuki Furuuchi: Non-Linearly Extended Self-Dual Relations From The Nambu-Bracket Description Of M5-Brane In A Constant C-Field Background, J. High Energ. Phys. 2010 127 (2010) [doi:10.1007/JHEP03(2010)127, arXiv:1001.2300]
Pei-Ming Ho, Chi-Hsien Yeh: D-brane in R-R Field Background, JHEP 1103:143 (2011) [doi:10.1007/JHEP03(2011)143, arXiv:1101.4054]
Pei-Ming Ho, Chen-Te Ma, Chi-Hsien Yeh: BPS States on M5-brane in Large $C$ -field Background, J. High Energ. Phys. 2012 76 (2012) [doi:10.1007/JHEP08(2012)076, arXiv:1206.1467]

The term “Nambu-Poisson-M5 brane model” is due to:

Chien-Ho Chen, Kazuyuki Furuuchi, Pei-Ming Ho, Tomohisa Takimi: 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) [doi:10.1007/JHEP10(2010)100, arXiv:1006.5291]
Andreas Gustavsson: M5 brane on $\mathbb{R}^{1,2} \times S^3$ , J. High Energ. Phys. 2012 57 (2012). [doi:10.1007/JHEP01(2012)057, arXiv:1111.5392]

More analysis towards the relation of the NP-M5 to the standard M5-brane sigma-model:

Review:

Pei-Ming Ho: A Concise Review on M5-brane in Large $C$ -Field Background, Chin. J. Phys. 48 1 (2010) [arXiv:0912.0445]
Pei-Ming Ho: Nambu-Poisson M5-Brane, talk notes (2011) [pdf, pdf]
Pei-Ming Ho, Yutaka Matsuo: Nambu bracket and M-theory, Progress of Theoretical and Experimental Physics 2016 6 (2016) 06A104 [doi:10.1093/ptep/ptw075, arXiv:1603.09534]