Bagger–Lambert–Gustavsson action

In theoretical physics, in the context of M-theory, the action for the N=8 M2 branes in full is (with some indices hidden):

${\displaystyle S=\int {\left(-{\frac {1}{2}}D^{\mu }X_{I}D_{\mu }X_{I}+{\frac {i}{2}}{\overline {\Psi }}\Gamma ^{\mu }D_{\mu }\Psi +{\frac {i}{4}}{\overline {\Psi }}\Gamma _{IJ}\left[X^{I},X^{J},\Psi \right]-{\frac {1}{12}}\left[X^{I},X^{J},X^{K}\right]\left[X^{I},X^{J},X^{K}\right]+{\frac {1}{2}}\varepsilon ^{abc}Tr(A_{a}\partial _{b}A_{c}+{\frac {2}{3}}A_{a}A_{b}A_{c})\right)}d\sigma ^{3}}$

where [, ] is a generalisation of a Lie bracket which gives the group constants.

The only known compatible solution however is:

${\displaystyle \left[A,B,C\right]_{\eta }\equiv \varepsilon ^{\mu \nu \tau \eta }A_{\mu }B_{\nu }C_{\tau }}$

using the Levi-Civita symbol which is invariant under SO(4) rotations. M5 branes can be introduced by using an infinite symmetry group.

The action is named after Jonathan Bagger, Neil Lambert, and Andreas Gustavsson.^[1][2][3]

Notes

References

• Lie 3-Algebra and Multiple M2-branes

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This page was last edited on 22 April 2023, at 05:01